A147766 Successive differences of A000990.

1, 0, 2, 2, 5, 6, 13, 16, 30, 40, 66, 90, 142, 192, 290, 396, 575, 782, 1112, 1500, 2092, 2808, 3848, 5132, 6945, 9192, 12298, 16178, 21422, 28000, 36763, 47748, 62205, 80334, 103910, 133458, 171538, 219150, 280039, 356020, 452469, 572548, 724047

Offset

0,3

Comments

Original definition: A000012^(-1) * A000990, where A000012^(-1) = the pairwise difference operator and A000990 = (1, 1, 3, 5, 10, 16, 29, 45, ...).

Triangle A147767 is constructed from A147766 in every column.

Links

Table of n, a(n) for n=0..42.

Formula

a(n) = A000990(n) - A000990(n-1) and a(0)=1.

G.f.: exp(2*Sum_{k>=1} (sigma_1(k) - 1)*x^k/k). - Ilya Gutkovskiy, Aug 21 2018

a(n) ~ exp(2*Pi*sqrt(n/3)) * Pi^2 / (4 * 3^(7/4) * n^(9/4)). - Vaclav Kotesovec, Aug 21 2018

Example

A000990 = (1, 1, 3, 5, 10, 16, ...). Pairwise differences = (1, 0, 2, 2, 5, ...).

Crossrefs

Cf. A000990, A147767.

Sequence in context: A098600 A181716 A261866 * A034420 A304867 A303931

Adjacent sequences: A147763 A147764 A147765 * A147767 A147768 A147769

Keyword

nonn

Author

Gary W. Adamson, Nov 11 2008

Extensions

Definition changed and more terms added by Olivier Gérard, Jul 25 2016

Status

approved