A162432 Row 3 of table A162430.

1, 6, 13, 25, 39, 52, 81, 97, 129, 154, 187, 234, 250, 321, 337, 406, 468, 493, 579, 613, 699, 766, 811, 918, 979, 1056, 1141, 1212, 1357, 1408, 1485, 1639, 1698, 1810, 1908, 2050, 2152, 2250, 2398, 2523, 2629, 2770, 2934, 2986, 3219, 3280, 3522, 3598, 3739

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..254

Formula

a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^3 for n>=0 where S(x) = Sum_{n>=0} x^(n(n+1)/2).

Example

The coefficients in the cube of the series:
S = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 +...
begin: [(1),(3,3),(4,6,3),(6,9,3,7),(9,6,9,9,6),(6,15,9,7,12,3),...];
the sums of the grouped coefficients yield the initial terms of this sequence.

Mathematica

t[n_, k_] := Module[{s = Sum[x^(m*(m+1)/2), {m, 0, k+1}] + O[x]^((k+1)*(k+2)/2)}, k*(k+1)/2+k}]]; Table[t[3, k], {k, 0, 48}] (* Jean-François Alcover, Nov 18 2013 *)

Prog

(PARI) {a(n)=local(S=sum(m=0, n+1, x^(m*(m+1)/2))+O(x^((n+1)*(n+2)/2))); sum(m=n*(n+1)/2, n*(n+1)/2+n, polcoeff(S^3, m))}

Crossrefs

Cf. A162430, A162431, A162433, A162434, A162435, A162426 (variant).

Sequence in context: A058535 A131833 A101736 * A117072 A081395 A343007

Adjacent sequences: A162429 A162430 A162431 * A162433 A162434 A162435

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2009

Status

approved