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A016153 (9^n-4^n)/5. 9
0, 1, 13, 133, 1261, 11605, 105469, 953317, 8596237, 77431669, 697147165, 6275373061, 56482551853, 508359743893, 4575304803901, 41178011670565, 370603178776909, 3335432903959477, 30018913315504477, 270170288559017029 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is also the coefficient of x^(n-1) in the bivariate Fibonacci polynomials F(n)(x,y)=xF(n-1)(x,y)+yF(n-2)(x,y),F(0)(x,y)=0,F(1)(x,y)=1, when we write 13x for x and -36x^2 for y. - Mario Catalani (mario.catalani(AT)unito.it), Dec 09 2002

LINKS

Table of n, a(n) for n=0..19.

R. Flórez, R. A. Higuita, A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).

Index entries for linear recurrences with constant coefficients, signature (13, -36).

FORMULA

G.f.: x/((1-4*x)*(1-9*x)). a(n)=13*a(n-1)-36*a(n-2).

a(n) = A015441(2*n).

MATHEMATICA

Join[{a=0, b=1}, Table[c=13*b-36*a; a=b; b=c, {n, 60}]](*and/or*)f[n_]:=(9^n-4^n)/5; f[Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)

PROG

(PARI) a(n)=(9^n-4^n)/5

CROSSREFS

Cf. A015441.

Sequence in context: A199144 A198664 A081042 * A187732 A031138 A097166

Adjacent sequences:  A016150 A016151 A016152 * A016154 A016155 A016156

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 18 09:09 EST 2017. Contains 294879 sequences.