(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):