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A169630
a(n) = n times the square of Fibonacci(n).
6
0, 1, 2, 12, 36, 125, 384, 1183, 3528, 10404, 30250, 87131, 248832, 705757, 1989806, 5581500, 15586704, 43356953, 120187008, 332134459, 915304500, 2516113236, 6900949462, 18888143927, 51599794176, 140718765625, 383142771674, 1041660829548, 2828107288188, 7668512468789
OFFSET
0,3
LINKS
G. Baron, H. Prodinger, R. F. Tichy, F. T. Boesch, and J. F. Wang, The number of spanning trees in the square of a cycle, Fibonacci Quart. 23 (1985), no. 3, 258-264 [MR0806296]
Zbigniew R. Bogdanowicz, The number of spanning trees in a superprism, Discrete Math. Lett. 13 (2024) 66-73. See Theorem 1.2.
R. Guy, Q on papers by Kleitman, Baron et al., SeqFan list, Mar 2010
D. J. Kleitman and B. Golden, Counting trees in a certain class of graphs, Amer. Math. Monthly 82 (1975), 40-44.
FORMULA
a(n) = A045925(n)*A000045(n) = n*A007598(n) = n *(A000045(n))^2.
a(n) = 4*a(n-1) -10*a(n-3) +4*a(n-5) -a(n-6).
G.f.: x*(1-2*x+4*x^2-2*x^3+x^4)/((1+x)^2*(x^2-3*x+1)^2).
a(n) = n*(((3 + sqrt(5))/2)^n + ((3 - sqrt(5))/2)^n - 2*(-1)^n)/5 (Bogdanowicz). - Stefano Spezia, May 05 2024
MAPLE
A169630 := proc(n) n*(combinat[fibonacci](n))^2 ; end proc:
MATHEMATICA
CoefficientList[Series[x*(1 - 2*x + 4*x^2 - 2*x^3 + x^4)/((1 + x)^2*(x^2 - 3*x + 1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)
Table[n Fibonacci[n]^2, {n, 0, 30}] (* or *) LinearRecurrence[{4, 0, -10, 0, 4, -1}, {0, 1, 2, 12, 36, 125}, 30] (* Harvey P. Dale, Jul 07 2017 *)
PROG
(Magma) I:=[0, 1, 2, 12, 36, 125]; [n le 6 select I[n] else 4*Self(n-1)-10*Self(n-3)+4*Self(n-5)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, Dec 19 2012
(Haskell)
a169630 n = a007598 n * n -- Reinhard Zumkeller, Sep 01 2013
(PARI) vector(40, n, n--; n*fibonacci(n)^2) \\ Michel Marcus, Jul 09 2015
CROSSREFS
Cf. A000045, A007598, A045925, A282464 (partial sums).
Sequence in context: A073404 A141208 A181825 * A192385 A352281 A361570
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 13 2010
STATUS
approved