(38G) OEIS A137442 & A167390

[Gerald H]

The programme installs symbolics to reproduce the sequence

http://oeis.org/A137442

in U1 & the partial sums

http://oeis.org/A167390

in U2.

Any functioning simpler version of the formulae would be welcome.

N^2 THEN LEAST UNLISTED

RUN SEQSET:
RECURSE(U,IFTE(N MOD 2,((N+1)/2)^2,U3(N/2)),1,2)►U1(N):
CHECK 1:
RECURSE(U,U6(N)*(1+U6(N)*(3+2*U6(N)))/6+U4(FLOOR(N/2)),1,3)►U2(N):
CHECK 2:
RECURSE(U,N+ROUND(√N,0),2,3)►U3(N):
RECURSE(U,U3(N)*(U3(N)+1)/2-U5(N)*(U5(N)+1)*(U5(N)+.5)/3,2,5)►U4(N):
RECURSE(U,FLOOR(√U3(N)),1,1)►U5(N):
RECURSE(U,CEILING(N/2),0,0)►U6(N):

SEQSET

SELECT Sequence:
UNCHECK 0:
0►NumFont:
0►Simult:
2►Angle:
1►InvCross:
1►NumStep:
1►Format:
1►NumCol:
1►NumStart:
6►NumRow:
RECURSE(U,0,0,0)►U1(N):
Ans►U2(N):
Ans►U3(N):
Ans►U4(N):
Ans►U5(N):
Ans►U6(N):
Ans►U7(N):
Ans►U8(N):
Ans►U9(N):
Ans►U0(N):

[rprosperi]

(04-10-2015 12:36 PM)Gerald H Wrote:  The programme installs symbolics to reproduce the sequence

http://oeis.org/A137442

in U1 & the partial sums

http://oeis.org/A167390

in U2.

Gerald - Pardon my mathemtical ignorance, but what are these sequences about, and how are they used and useful? I've no experience at all with sequences and without context I can't imagine how they apply to anything real, with absolutely no offense meant at all.

[Gerald H]

I found the first sequence by chance & found it pretty, prompting me to find a short expression for the partial sums.

I know of no practical application where these two sequences prove useful, but this probably just attests to the simplicity of my lifestyle.

The sequences certainly apply to themselves, if you wish to find the sum of the first 10,000 terms you can do this on the miserable 38G using the formulae.

I can't think of anything that is more real than these sequences, they're there, just like a zebra.

Finding order in the disorderly & making a map to guide us along the erratic path is my idea of fun.

Have a look at these pictures by an Austrian artist

http://www.gleich.at/

The pictures are formal, ie they represent themselves, they aren't pictures of anything, they just are.

That's my feeling about these sequences.

[rprosperi]

(04-10-2015 03:37 PM)Gerald H Wrote:  I found the first sequence by chance & found it pretty, prompting me to find a short expression for the partial sums.

I know of no practical application where these two sequences prove useful, but this probably just attests to the simplicity of my lifestyle.

The sequences certainly apply to themselves, if you wish to find the sum of the first 10,000 terms you can do this on the miserable 38G using the formulae.

I can't think of anything that is more real than these sequences, they're there, just like a zebra.

Finding order in the disorderly & making a map to guide us along the erratic path is my idea of fun.

Have a look at these pictures by an Austrian artist

http://www.gleich.at/

The pictures are formal, ie they represent themselves, they aren't pictures of anything, they just are.

That's my feeling about these sequences.

Thanks for clarifying Gerald. Understand that in my view, having no practical application in no way means it isn't interesting nor that it shouldn't be studied or analyzed, I simply had not seen such sequences analyzed or calculated before, and have no idea what they're about.

Indeed, very little of what I do with these machines is in any way relevant to real problem solving. Like you it seems, I explore it because it's interesting to explore.

By all means, keep it up, you seem to be good at it.