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A051959 Expansion of (1+6x)/( (1-2x-x^2)(1-x)^2). 1
1, 10, 36, 104, 273, 686, 1688, 4112, 9969, 24114, 58268, 140728, 339809, 820438, 1980784, 4782112, 11545121, 27872474, 67290196, 162453000, 392196337, 946845822, 2285888136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

A. F. Horadam, Special Properties of the Sequence W(n){a,b; p,q}, Fib. Quart., Vol. 5, No. 5 (1967), pp. 424-434.

Index entries for linear recurrences with constant coefficients, signature (4,-4,0,1).

FORMULA

a(n) = 2a(n-1) + a(n-2) + (7n+1); a(0)=1, a(1)=10.

a(n) = ((((25/2)+17*sqrt(2)/2)(1+sqrt(2))^n - ((25/2)-17*sqrt(2)/2)(1-sqrt(2))^n)/2*sqrt(2)) - (7n+15)/2

(1/2) (4*Pell(n+2) - 3*Pell(n) - 7n - 15), with Pell(n) = A000129(n). - Ralf Stephan, May 15 2007

a(n) = 4*a(n-1) - 4*a(n-2) + a(n-4).

MATHEMATICA

LinearRecurrence[{4, -4, 0, 1}, {1, 10, 36, 104}, 40] (* Vincenzo Librandi, Jun 22 2012 *)

PROG

(MAGMA) I:=[1, 10, 36, 104]; [n le 4 select I[n] else 4*Self(n-1)-4*Self(n-2)+Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 22 2012

CROSSREFS

Cf. A048771, A048695.

Sequence in context: A050509 A211057 A118415 * A117327 A153371 A248463

Adjacent sequences:  A051956 A051957 A051958 * A051960 A051961 A051962

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jan 04 2000

STATUS

approved

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Last modified May 11 13:41 EDT 2021. Contains 343791 sequences. (Running on oeis4.)