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A171067 G.f. -x*(x-1)*(1+x)/((x^2+3*x+1)*(x^2-4*x+1)). 1
0, 1, 1, 10, 21, 121, 340, 1561, 5061, 20890, 72721, 285121, 1028160, 3931201, 14425201, 54480250, 201635301, 756931801, 2813339860, 10529812921, 39218508021, 146573045290, 546474598561, 2040893746561, 7612994269440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The member k=10 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 (1,10,1,-1).

FORMULA

a(n)= +a(n-1) +10*a(n-2) +a(n-3) -a(n-4).

a(n)= -(-1)^n*A005248(n)/7 + 2*A001075(n)/7.

MATHEMATICA

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

LinearRecurrence[{1, 10, 1, -1}, {0, 1, 1, 10}, 30] (* Harvey P. Dale, Dec 24 2017 *)

PROG

(MAGMA) I:=[0, 1, 1, 10]; [n le 4 select I[n] else Self(n-1) + 10*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: A001739 A072805 A119033 * A121807 A133163 A242831

Adjacent sequences:  A171064 A171065 A171066 * A171068 A171069 A171070

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 22 06:32 EDT 2019. Contains 323478 sequences. (Running on oeis4.)