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A016153
a(n) = (9^n-4^n)/5.
11
0, 1, 13, 133, 1261, 11605, 105469, 953317, 8596237, 77431669, 697147165, 6275373061, 56482551853, 508359743893, 4575304803901, 41178011670565, 370603178776909, 3335432903959477, 30018913315504477, 270170288559017029
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
R. Flórez, R. A. Higuita and A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).
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: A332243 A081042 A329019 * A187732 A031138 A360190
KEYWORD
nonn,easy
AUTHOR
STATUS
approved