A135901 Number of terms in row n of irregular triangle A135879 for n>=0.

1, 2, 4, 7, 12, 18, 26, 36, 47, 60, 75, 92, 111, 132, 154, 178, 204, 232, 262, 294, 328, 364, 402, 442, 484, 527, 572, 619, 668, 719, 772, 827, 884, 943, 1004, 1067, 1132, 1199, 1268, 1339, 1412, 1487, 1564, 1643, 1724, 1807, 1892, 1978, 2066, 2156, 2248

Offset

0,2

Links

Table of n, a(n) for n=0..50.

Formula

G.f.: A(x) = (1+x^2)/(1-x)^3 - [Sum_{n>=1} x^b(n)]/(1-x)^2, where b(n) = (2^(n+1) + 6*n + 3 + (-1)^n)/12.

Example

A(x) = (1+x^2)/(1-x)^3 - [x+x^2+x^3+x^5+x^8+x^14+x^25+x^47+x^90+x^176+...]/(1-x)^2.

Prog

(PARI) {a(n)=polcoeff((1+x^2)/(1-x+x*O(x^n))^3 - sum(k=1, #binary(n)+2, x^((2^(k+1)+6*k+3+(-1)^k)/12))/(1-x +x*O(x^n) )^2, n)}

Crossrefs

Cf. A135879.

Sequence in context: A227590 A267529 A005521 * A124197 A011909 A065962

Adjacent sequences: A135898 A135899 A135900 * A135902 A135903 A135904

Keyword

nonn

Author

Paul D. Hanna, Dec 16 2007

Status

approved