A140796 a(n)=a(n-1)+6a(n-2), n>2.

1, 5, 14, 44, 128, 392, 1160, 3512, 10472, 31544, 94376, 283640, 849896, 2551736, 7651112, 22961528, 68868200, 206637368, 619846568, 1859670776, 5578750184, 16736774840, 50209275944, 150629924984, 451885580648, 1355665130552

Offset: 0

Author

Paul Curtz, Jul 15 2008

Keywords

• nonn

Comments

The binomial transform is A037481.

The recurrence of the definition is also satisfied by A087451, A102901 and A140725.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 6).

Crossrefs

Cf. A140725

Programs

Mathematica

Join[{1},LinearRecurrence[{1,6},{5,14},30]] (* Harvey P. Dale, Nov 20 2011 *)

Formula

a(n+1)-3a(n) = (-1)^n*A000079(n-1), n>0.

d(n+1)-3d(n) = (-1)^(n+1)*A000079(n-1), n>0, where d(n) is the sequence of pair sums d(n)= a(n)+a(n+1)=6, 19, 58, 172,...

O.g.f.: (1+x)(3x+1)/((2x+1)(1-3x)). - R. J. Mathar, Jul 29 2008

a(n) = (-1)^(n+1)*2^n/10+8*3^n/5, n>0. - R. J. Mathar, Jul 29 2008

a(n) = A140725(n)+A140725(n+1). - Philippe Deléham, Nov 17 2013

Extensions

Edited and extended by R. J. Mathar, Jul 29 2008