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

Author

Paul Barry, Jun 12 2003

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A004277.

Programs

Mathematica

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

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