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A100505 Bisection of A001523. 3

%I

%S 1,2,8,27,79,209,512,1183,2604,5504,11240,22277,43003,81098,149769,

%T 271404,483439,847681,1464999,2498258,4207764,7005688,11538936,

%U 18814423,30387207,48641220,77205488,121567834,189974638,294742961,454164484

%N Bisection of A001523.

%H Alois P. Heinz, <a href="/A100505/b100505.txt">Table of n, a(n) for n = 0..5000</a>

%p 1,seq(coeff(convert(series(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=1..45); (C. Ronaldo)

%p # second Maple program:

%p b:= proc(n, i) option remember;

%p `if`(i>n, 0, `if`(irem(n, i)=0, 1, 0)+

%p add(b(n-i*j, i+1)*(j+1), j=0..n/i))

%p end:

%p a:= n-> `if`(n=0, 1, b(2*n, 1)):

%p seq(a(n), n=0..60); # _Alois P. Heinz_, Mar 26 2014

%t 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-Fran├žois Alcover_, Apr 04 2017 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 24 2004

%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)