A080920 a(n) = 2*a(n-1) + 35*a(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, 46585225103457261, 325619738565997702, 2281722355752999539

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (2,35).

Formula

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

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

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

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

E.g.f.: exp(x) * sinh(6*x) / 6. - Amiram Eldar, Dec 28 2025

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 *)

Crossrefs

Cf. A015441, A051958, A079773, A238801.

Sequence in context: A201360 A227904 A175760 * A086338 A329552 A042683

Adjacent sequences: A080917 A080918 A080919 * A080921 A080922 A080923

Keyword

easy,nonn

Author

Paul Barry, Feb 24 2003

Status

approved