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A215466 Expansion of x*(1-4*x+x^2) / ( (x^2-7*x+1)*(x^2-3*x+1) ). 11
0, 1, 6, 38, 252, 1705, 11628, 79547, 544824, 3733234, 25585230, 175356611, 1201893336, 8237850373, 56462937882, 387002396990, 2652553009008, 18180866487757, 124613506702404, 854113665498719, 5854182112700460 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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

H. C. Williams and R. K. Guy, Odd and even linear divisibility sequences of order 4, INTEGERS, 2015, #A33.

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (10,-23,10,-1).

FORMULA

a(n) = L(n)*F(3n)/4 if n even, = F(n)*L(3n)/4 if n odd, where L=A000032, F=A000045.

a(n) = 3*A004187(n)/4 + A001906(n)/4.

a(n) = 10*a(n-1)-23*a(n-2)+10*a(n-3)-a(n-4), a(0)=0, a(1)=1, a(2)=6, a(3)=38. - Harvey P. Dale, Nov 02 2015

MAPLE

A215466 := proc(n)

    if type(n, 'even') then

        A000032(n)*combinat[fibonacci](3*n)/4 ;

    else

        combinat[fibonacci](n)*A000032(3*n)/4 ;

    end if;

end proc:

MATHEMATICA

CoefficientList[Series[x*(1 - 4*x + x^2)/((x^2 - 7*x + 1)*(x^2 - 3*x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 23 2012 *)

LinearRecurrence[{10, -23, 10, -1}, {0, 1, 6, 38}, 30] (* Harvey P. Dale, Nov 02 2015 *)

PROG

(MAGMA) I:=[0, 1, 6, 38]; [n le 4 select I[n] else 10*Self(n-1)-23*Self(n-2)+10*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 23 2012

(MAGMA) /* By definition: "/ m:=20; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1-4*x+x^2)/((x^2-7*x+1)*(x^2-3*x+1)))); // Bruno Berselli, Dec 24 2012

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 10, -23, 10]^n*[0; 1; 6; 38])[1, 1] \\ Charles R Greathouse IV, Nov 13 2015

CROSSREFS

Sequence in context: A135030 A217633 A162558 * A147957 A098410 A079949

Adjacent sequences:  A215463 A215464 A215465 * A215467 A215468 A215469

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Aug 11 2012

STATUS

approved

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)