A084859 Binomial transform of Cullen numbers A002064.

1, 4, 16, 62, 232, 842, 2980, 10334, 35248, 118610, 394684, 1301126, 4255624, 13825658, 44657428, 143521838, 459230560, 1463719586, 4649308012, 14722502870, 46491507256, 146447041994, 460259735236, 1443537130622

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (8,-21,18).

Formula

a(n)=2^n+2n*3^(n-1); a(n)=sum{k=0..n, C(n, k)(1+k*2^k) }.

O.g.f.: (1-4x+5x^2)/[(1-2x)(-1+3x)^2]. - R. J. Mathar, Apr 02 2008

a(0)=1, a(1)=4, a(2)=16, a(n)=8*a(n-1)-21*a(n-2)+18*a(n-3). - Harvey P. Dale, Mar 31 2015

Mathematica

LinearRecurrence[{8, -21, 18}, {1, 4, 16}, 30] (* Harvey P. Dale, Mar 31 2015 *)

Crossrefs

Cf. A004277.

Sequence in context: A365835 A365860 A276042 * A081666 A250346 A085781

Adjacent sequences: A084856 A084857 A084858 * A084860 A084861 A084862

Keyword

easy,nonn

Author

Paul Barry, Jun 12 2003

Status

approved