A169630 a(n) = n times the square of Fibonacci(n).

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

Offset

0,3

Links

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

G. Baron, H. Prodinger, R. F. Tichy, F. T. Boesch, J. F. Wang, The number of spanning trees in the square of a cycle, Fibonacci Quart. 23 (1985), no. 3, 258-264 [MR0806296]

R. Guy, Q on papers by Kleitman, Baron et al., SeqFan list, Mar 2010

D. J. Kleitman, B. Golden, Counting trees in a certain class of graphs, Amer. Math. Monthly 82 (1975), 40-44.

Index entries for linear recurrences with constant coefficients, signature (4,0,-10,0,4,-1)

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).

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

Adjacent sequences: A169627 A169628 A169629 * A169631 A169632 A169633

Keyword

nonn,easy

Author

R. J. Mathar, Mar 13 2010

Status

approved