A182153 G.f.: [Sum_{n>=0} x^(n^2) * (1+x+x^2)^n ]^2.

1, 2, 3, 4, 5, 8, 13, 16, 17, 18, 24, 38, 53, 62, 64, 68, 83, 108, 135, 158, 181, 214, 264, 326, 383, 412, 408, 402, 457, 620, 871, 1124, 1285, 1326, 1292, 1266, 1322, 1524, 1920, 2504, 3165, 3696, 3916, 3818, 3644, 3772, 4492, 5796, 7363, 8748, 9643, 10014, 10031

Offset

0,2

Comments

Equals the self-convolution of the flattened triangle of trinomial coefficients (A027907).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1024

Formula

G.f.: [Sum_{n>=0} (1+x+x^2)^n*x^n * Product_{k=1..n} (1 - (1+x+x^2)*x^(4*k-3))/(1 - (1+x+x^2)*x^(4*k-1)) ]^2.

Example

G.f.: A(x) = 1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 8*x^5 + 13*x^6 + 16*x^7 + 17*x^8 + 18*x^9 +...
such that
A(x)^(1/2) = 1 + x*(1+x+x^2) + x^4*(1+x+x^2)^2 + x^9*(1+x+x^2)^3 + x^16*(1+x+x^2)^4 +...

Prog

(PARI) {a(n)=local(A=sum(m=0, sqrtint(n+1), x^(m^2)*(1+x+x^2+x*O(x^n))^m)); polcoeff(A^2, n)}
for(n=0, 66, print1(a(n), ", "))

Crossrefs

Cf. A152037, A027907.

Sequence in context: A373895 A347333 A050024 * A230771 A065490 A214452

Adjacent sequences: A182150 A182151 A182152 * A182154 A182155 A182156

Keyword

nonn

Author

Paul D. Hanna, Apr 18 2012

Status

approved