This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.