A080920 a(n) = 2a(n-1) + 35a(n-2), a(0)=0, a(1)=1.

0, 1, 2, 39, 148, 1661, 8502, 75139, 447848, 3525561, 22725802, 168846239, 1133095548, 8175809461, 56009963102, 398173257339, 2756695223248, 19449454453361, 135383241720402, 951497389308439, 6641408238830948

Offset: 0

Author

Paul Barry, Feb 24 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (2,35).

Crossrefs

Cf. A079773, A051958, A015441.

Programs

Mathematica

Join[{a=0,b=1},Table[c=2*b+35*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
CoefficientList[Series[1 / ((1 + 5 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 05 2013 *)
LinearRecurrence[{2,35},{0,1},30] (* Harvey P. Dale, Aug 24 2017 *)

Formula

a(n) = 7^n/12 - (-5)^n/12.

a(n) = Sum{k=1..n, binomial(n, 2k-1)*6^(2(k-1))}.

G.f.: 1/((1+5x)(1-7x)).

a(n+1) = Sum_{k = 0..n} A238801(n,k)*6^k. - Philippe Deléham, Mar 07 2014