A144044 - OEIS

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A144044

a(n) = ((1+sqrt(11))^n-(1-sqrt(11))^n)^2/44.

1, 4, 196, 2304, 55696, 906304, 18181696, 325730304, 6199357696, 114211554304, 2141141533696, 39766241378304, 742275639709696, 13817991215202304, 257604225193885696, 4798702283133026304, 89428432275804061696

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OFFSET

1,2

COMMENTS

Sequences of the form a(n) = ((A+sqrt B)^n-(A-sqrt B)^n)^2/(4B) have recurrences a(n) = (3A^2+B) *a(n-1) +(B+3A^2)*(B-A^2) *a(n-2) -(B-A^2)^3*a(n-3) and generating functions x(1+(A^2-B)x) / ((1 -(A^2-B)x)(1-2(A^2+B)x +(A^4-2A^2B+B^2)x^2)). - R. J. Mathar, Nov 01 2008

LINKS

Table of n, a(n) for n=1..17.

Index entries for linear recurrences with constant coefficients, signature (14,140,-1000).

FORMULA

From R. J. Mathar, Nov 01 2008: (Start)

a(n) = 14*a(n-1)+140*a(n-2)-1000*a(n-3).

G.f. x(1-10x)/((10x+1)(1-24x+100x^2)). (End)

CROSSREFS

Sequence in context: A383255 A219163 A017546 * A221197 A180991 A279803

Adjacent sequences: A144041 A144042 A144043 * A144045 A144046 A144047

KEYWORD

nonn,easy