A086950 Binomial transform of decagonal numbers A001107.

0, 1, 12, 60, 224, 720, 2112, 5824, 15360, 39168, 97280, 236544, 565248, 1331200, 3096576, 7127040, 16252928, 36765696, 82575360, 184287232, 408944640, 902823936, 1983905792, 4341104640, 9462349824, 20552089600, 44493176832, 96032784384, 206695301120, 443723808768

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Formula

a(n) = n*2^n*(2*n-1)/2.

G.f.: x*(1+6*x)/(1-2*x)^3.

a(0)=0, a(1)=1, a(2)=12, a(n)=6*a(n-1)-12*a(n-2)+8*a(n-3). - Harvey P. Dale, Dec 13 2015

E.g.f.: exp(2*x)*x*(1 + 4*x). - Stefano Spezia, Oct 09 2022

Mathematica

LinearRecurrence[{6, -12, 8}, {0, 1, 12}, 30] (* Harvey P. Dale, Dec 13 2015 *)

Prog

(Magma) [n*2^n*(2*n-1)/2: n in [0..30] ]; // Vincenzo Librandi, Aug 22 2011

Crossrefs

Binomial transform is A086951.

Sequence in context: A012582 A260356 A120571 * A370700 A074433 A280175

Adjacent sequences: A086947 A086948 A086949 * A086951 A086952 A086953

Keyword

easy,nonn

Author

Paul Barry, Jul 24 2003

Status

approved