A004797 Convolution of A002024 with itself.

1, 4, 8, 14, 22, 30, 41, 54, 67, 82, 99, 118, 138, 160, 182, 206, 234, 262, 292, 322, 353, 388, 425, 462, 501, 542, 583, 626, 671, 718, 766, 818, 870, 922, 976, 1030, 1088, 1148, 1210, 1274, 1338, 1402, 1469, 1538, 1607, 1678, 1753, 1828, 1905, 1984, 2063

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• Raphael Schumacher, The self-counting identity, Fib. Quart., 55 (No. 2 2017), 157-167.

Crossrefs

Cf. A002024.

Programs

Maple

a002024:= [seq(i$i,i=1..10)]:
g002024:= add(a002024[i]*x^(i-1),i=1..nops(a002024)):
g:= expand(g002024^2):
seq(coeff(g,x,i),i=0..degree(g002024)); # Robert Israel, May 30 2017

PARI

nn(n)=(sqrtint(n*8)+1)\2;
a(n) = sum(k=1, n, nn(k)*nn(n-k+1)); \\ Michel Marcus, May 30 2017

Formula

G.f.: (1/(1 - x)^2)*Product_{k>=1} (1 - x^(2*k))^2/(1 - x^(2*k-1))^2. - Ilya Gutkovskiy, May 30 2017