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A015559 Expansion of x/(1-7x-3x^2). 3
0, 1, 7, 52, 385, 2851, 21112, 156337, 1157695, 8572876, 63483217, 470101147, 3481157680, 25778407201, 190892323447, 1413581485732, 10467747370465, 77514976050451, 574008074464552, 4250601449403217, 31476234369216175 (list; graph; refs; listen; history; text; internal format)
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 xrange(0, 21)]# [From 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

CROSSREFS

Sequence in context: A037593 A037684 A246513 * A097180 A259554 A147962

Adjacent sequences:  A015556 A015557 A015558 * A015560 A015561 A015562

KEYWORD

nonn,easy,changed

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 22 10:40 EST 2017. Contains 295087 sequences.