The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A100505 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A100505

Bisection of A001523.
(history; published version)

#19 by Michael De Vlieger at Tue Apr 04 07:46:37 EDT 2023

STATUS

reviewed

approved

#18 by Michel Marcus at Tue Apr 04 01:53:41 EDT 2023

STATUS

proposed

reviewed

#17 by Alois P. Heinz at Mon Apr 03 14:22:43 EDT 2023

STATUS

editing

proposed

#16 by Alois P. Heinz at Mon Apr 03 14:22:10 EDT 2023

DATA

1, 2, 8, 27, 79, 209, 512, 1183, 2604, 5504, 11240, 22277, 43003, 81098, 149769, 271404, 483439, 847681, 1464999, 2498258, 4207764, 7005688, 11538936, 18814423, 30387207, 48641220, 77205488, 121567834, 189974638, 294742961, 454164484, 695254782, 1057704607

#15 by Alois P. Heinz at Mon Apr 03 14:21:00 EDT 2023

MAPLE

1, seq(coeff(convert(series(1+add(-(-1)^k*x^(k*(k+1)/2), k=1..100)/(mul(1-x^k, k=1..100))^2, x, 100), polynom), x, 2*n), n=10..45); # (C. Ronaldo)

STATUS

proposed

editing

#14 by G. C. Greubel at Mon Apr 03 14:13:43 EDT 2023

STATUS

editing

proposed

#13 by G. C. Greubel at Mon Apr 03 14:13:35 EDT 2023

PROG

(Magma)

m:=200;

R<x>:=PowerSeriesRing(Integers(), m);

b:=Coefficients(R!( 1 + (&+[ x^n*(1-x^n)/(&*[(1-x^j)^2: j in [1..n]]): n in [1..m+2]]) ));

A100505:= func< n | b[2*n+1] >;

[A100505(n): n in [0..80]]; // G. C. Greubel, Apr 03 2023

(SageMath)

@CachedFunction

def b(n, k): # Indranil Ghosh's code of A001523

if k>n: return 0

if n%k==0: x=1

else: x=0

return x + sum(b(n-k*j, k+1)*(j+1) for j in range(n//k + 1))

def A100505(n): return 1 if n==0 else b(2*n, 1)

[A100505(n) for n in range(81)] # G. C. Greubel, Apr 03 2023

CROSSREFS

Cf. A001523, A100506.

STATUS

approved

editing

#12 by Bruno Berselli at Tue Apr 04 08:06:47 EDT 2017

STATUS

proposed

approved

#11 by Jean-François Alcover at Tue Apr 04 07:53:18 EDT 2017

STATUS

editing

proposed

#10 by Jean-François Alcover at Tue Apr 04 07:53:12 EDT 2017

MATHEMATICA

max = 70; s = 1 + Sum[(-1)^(k+1)*q^(k*(k+1)/2), {k, 1, Sqrt[2 max] // Ceiling}]/QPochhammer[q]^2 + O[q]^max // Normal; Partition[(List @@ s) /. q -> 1, 2][[All, 1]] (* Jean-François Alcover, Apr 04 2017 *)

STATUS

approved

editing