A015559 Expansion of x/(1 - 7*x - 3*x^2).

0, 1, 7, 52, 385, 2851, 21112, 156337, 1157695, 8572876, 63483217, 470101147, 3481157680, 25778407201, 190892323447, 1413581485732, 10467747370465, 77514976050451, 574008074464552, 4250601449403217, 31476234369216175

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,3).

Formula

a(n) = 7*a(n-1) + 3*a(n-2).

a(n) = (1/61)*sqrt(61)*(7/2 + (1/2)*sqrt(61))^n - (1/61)*(7/2 - (1/2)*sqrt(61))^n*sqrt(61), with n >= 0. - Paolo P. Lava, Jun 25 2008

Mathematica

Join[{a=0, b=1}, Table[c=7*b+3*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{7, 3}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
CoefficientList[Series[x/(1-7x-3x^2), {x, 0, 30}], x] (* Harvey P. Dale, Nov 12 2017 *)

Prog

(Sage) [lucas_number1(n, 7, -3) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(Magma) [n le 2 select n-1 else 7*Self(n-1) + 3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-7*x-3*x^2))) \\ G. C. Greubel, Dec 30 2017

Crossrefs

Sequence in context: A037593 A037684 A246513 * A097180 A259554 A147962

Adjacent sequences: A015556 A015557 A015558 * A015560 A015561 A015562

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved