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A015568 Expansion of x/(1 - 7*x - 10*x^2). 2
0, 1, 7, 59, 483, 3971, 32627, 268099, 2202963, 18101731, 148741747, 1222209539, 10042884243, 82522285091, 678084838067, 5571816717379, 45783565402323, 376203124990051, 3091257528953587, 25400833952575619, 208718412957565203, 1715037230228712611, 14092444741176640307 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Pisano period lengths: 1, 1, 8, 1, 4, 8, 12, 1, 24, 4, 5, 8, 21, 12, 8, 1, 16, 24, 45, 4, ... - R. J. Mathar, Aug 10 2012

Number of compositions of n-1 into parts 1 (of 7 sorts) and 2 (of 10 sorts). - Joerg Arndt, Oct 15 2013

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (7,10).

FORMULA

a(n) = 7*a(n-1) + 10*a(n-2).

a(n) = -(1/89)*(7/2 - (1/2)*sqrt(89))^n*sqrt(89) + (1/89)*sqrt(89)*(7/2  + (1/2)*sqrt(89))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008

G.f.: Q(0)*x/(2-7*x), where Q(k) = 1 + 1/( 1 - x*(89*k-49)/( x*(89*k+40) - 14/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Oct 14 2013

MATHEMATICA

Join[{a=0, b=1}, Table[c=7*b+10*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)

LinearRecurrence[{7, 10}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 7, -10) for n in range(0, 20)] # Zerinvary Lajos, Apr 24 2009

(MAGMA) [n le 2 select n-1 else 7*Self(n-1) + 10*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-10*x^2))) \\ G. C. Greubel, Jan 06 2018

CROSSREFS

Sequence in context: A236070 A059705 A218201 * A322667 A101487 A210397

Adjacent sequences:  A015565 A015566 A015567 * A015569 A015570 A015571

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified January 20 10:18 EST 2022. Contains 350471 sequences. (Running on oeis4.)