A100506 Bisection of A001523.

1, 4, 15, 47, 130, 330, 784, 1765, 3804, 7898, 15880, 31048, 59220, 110484, 202070, 362974, 641368, 1116325, 1916184, 3247088, 5436972, 9002752, 14752316, 23938188, 38487496, 61344055, 96974176, 152110204, 236837795, 366177506, 562373990, 858193804, 1301654610

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Maple

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+1), n=0..45); # (C. Ronaldo)
# second Maple program:
b:= proc(n, i) option remember;
      `if`(i>n, 0, `if`(irem(n, i)=0, 1, 0)+
      add(b(n-i*j, i+1)*(j+1), j=0..n/i))
    end:
a:= n-> `if`(n=0, 1, b(2*n+1, 1)):
seq(a(n), n=0..60);  # Alois P. Heinz, Mar 26 2014

Mathematica

b[n_, i_]:= b[n, i]= If[i>n, 0, If[Mod[n, i]==0, 1, 0] + Sum[b[n-i*j, i + 1]*(j+1), {j, 0, n/i}]];
a[n_]:= If[n==0, 1, b[2*n+1, 1]];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Jun 18 2018, after Alois P. Heinz *)

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]]) ));
A100506:= func< n | b[2*n+2] >;
[A100506(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 A100506(n): return 1 if n==0 else b(2*n+1, 1)
[A100506(n) for n in range(41)] # G. C. Greubel, Apr 03 2023

Crossrefs

Cf. A001523.

Sequence in context: A195688 A111038 A188716 * A173414 A307075 A219903

Adjacent sequences: A100503 A100504 A100505 * A100507 A100508 A100509

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 24 2004

Extensions

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

Status

approved