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A171069 G.f. -x*(x-1)*(1+x)/(1-x-12*x^2-x^3+x^4). 1
0, 1, 1, 12, 25, 169, 480, 2521, 8425, 38988, 142129, 615889, 2352000, 9845809, 38543569, 158429388, 628446025, 2558296441, 10219534560, 41389108489, 165953373625, 670283913612, 2692893971041, 10860865199521, 43679923392000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The member k=12 of a family of sequences starting 0,1,1,k with recurrence a(n) = a(n-1)+k*a(n-2)+a(n-3)-a(n-4).

LINKS

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

Hugh Williams, R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory vol. 7 (5) (2011) 1255-1277

Index entries for linear recurrences with constant coefficients, signature (1,12,1,-1).

FORMULA

a(n)= +a(n-1) +12*a(n-2) +a(n-3) -a(n-4).

MATHEMATICA

CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 12*x^2 - x^3 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)

PROG

(MAGMA) I:=[0, 1, 1, 12]; [n le 4 select I[n] else Self(n-1) + 12*Self(n-2) + Self(n-3) - Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 19 2012

CROSSREFS

Cf. A116201 (k=1), A105309 (k=2), A152090 (k=3), A007598 (k=4), A005178 (k=5), A003757 (k=6).

Sequence in context: A041282 A195116 A041284 * A042193 A041286 A025138

Adjacent sequences:  A171066 A171067 A171068 * A171070 A171071 A171072

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, at the request of R. K. Guy, Sep 03 2010

STATUS

approved

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Last modified April 20 17:54 EDT 2019. Contains 322310 sequences. (Running on oeis4.)