A162426 Row 3 of table A162424.

1, 3, 6, 13, 24, 34, 49, 69, 94, 117, 148, 174, 211, 249, 298, 331, 366, 439, 498, 535, 591, 670, 733, 792, 880, 939, 1006, 1123, 1212, 1270, 1353, 1456, 1599, 1648, 1750, 1896, 1963, 2127, 2164, 2379, 2452, 2545, 2709, 2848, 2997, 3094, 3276, 3385, 3595

Offset

0,2

Links

Table of n, a(n) for n=0..48.

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+1)(n+2)/2-1).

Example

The coefficients in the cube of the series:
S = 1 + x^2 + x^5 + x^9 + x^14 + x^20 + x^27 + x^35 + x^44 +...
begin: [(1),(0,3),(0,3,3),(1,6,0,6),(3,6,3,3,9),(1,12,0,6,9,6),...];
the sums of the grouped coefficients yield the initial terms of this sequence.

Prog

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

Crossrefs

Cf. A162424, A162425, A162427, A162428, A162429; A162432 (variant).

Sequence in context: A323580 A002799 A285263 * A058554 A342646 A342853

Adjacent sequences: A162423 A162424 A162425 * A162427 A162428 A162429

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2009

Status

approved