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A171066 G.f. -x*(x-1)*(1+x)/(1-x-9*x^2-x^3+x^4). 1
0, 1, 1, 9, 19, 100, 279, 1189, 3781, 14661, 49600, 184141, 641421, 2333629, 8240959, 29700900, 105561739, 378777169, 1350292761, 4835148121, 17260998400, 61748847081, 220582688041, 788748162049, 2818480203099, 10076047502500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The member k=9 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 (1,9,1,-1).

FORMULA

a(n)= +a(n-1) +9*a(n-2) +a(n-3) -a(n-4)

MATHEMATICA

CoefficientList[Series[-x*(x - 1)*(1 + x)/(1 - x - 9*x^2 - x^3 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)

PROG

(MAGMA) I:=[0, 1, 1, 9]; [n le 4 select I[n] else Self(n-1) + 9*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: A186508 A000981 A060227 * A068174 A165247 A177130

Adjacent sequences:  A171063 A171064 A171065 * A171067 A171068 A171069

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 May 20 20:16 EDT 2019. Contains 323426 sequences. (Running on oeis4.)