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A169630 a(n) = n times the square of Fibonacci(n). 4
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 (list; graph; refs; listen; history; text; internal format)
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. A282464 (partial sums).

Sequence in context: A073404 A141208 A181825 * A192385 A294464 A185788

Adjacent sequences:  A169627 A169628 A169629 * A169631 A169632 A169633

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Mar 13 2010

STATUS

approved

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Last modified November 23 20:23 EST 2017. Contains 295141 sequences.