This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A169630 #53 Jan 05 2025 19:51:39
%S A169630 0,1,2,12,36,125,384,1183,3528,10404,30250,87131,248832,705757,
%T A169630 1989806,5581500,15586704,43356953,120187008,332134459,915304500,
%U A169630 2516113236,6900949462,18888143927,51599794176,140718765625,383142771674,1041660829548,2828107288188,7668512468789
%N A169630 a(n) = n times the square of Fibonacci(n).
%H A169630 Vincenzo Librandi, <a href="/A169630/b169630.txt">Table of n, a(n) for n = 0..1000</a>
%H A169630 G. Baron, H. Prodinger, R. F. Tichy, F. T. Boesch, and J. F. Wang, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/23-3/baron.pdf">The number of spanning trees in the square of a cycle</a>, Fibonacci Quart. 23 (1985), no. 3, 258-264 [<a href="http://www.ams.org/mathscinet-getitem?mr=806296">MR0806296</a>]
%H A169630 Zbigniew R. Bogdanowicz, <a href="https://www.dmlett.com/archive/v13/DML24_v13_pp66-73.pdf">The number of spanning trees in a superprism</a>, Discrete Math. Lett. 13 (2024) 66-73. See Theorem 1.2.
%H A169630 R. Guy, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2010-March/003959.html">Q on papers by Kleitman, Baron et al.</a>, SeqFan list, Mar 2010
%H A169630 D. J. Kleitman and B. Golden, <a href="http://www.jstor.org/stable/2319131">Counting trees in a certain class of graphs</a>, Amer. Math. Monthly 82 (1975), 40-44.
%H A169630 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-10,0,4,-1).
%F A169630 a(n) = A045925(n)*A000045(n) = n*A007598(n) = n *(A000045(n))^2.
%F A169630 a(n) = 4*a(n-1) -10*a(n-3) +4*a(n-5) -a(n-6).
%F A169630 G.f.: x*(1-2*x+4*x^2-2*x^3+x^4)/((1+x)^2*(x^2-3*x+1)^2).
%F A169630 a(n) = n*(((3 + sqrt(5))/2)^n + ((3 - sqrt(5))/2)^n - 2*(-1)^n)/5 (Bogdanowicz). - _Stefano Spezia_, May 05 2024
%p A169630 A169630 := proc(n) n*(combinat[fibonacci](n))^2 ; end proc:
%t A169630 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 *)
%t A169630 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 *)
%o A169630 (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
%o A169630 (Haskell)
%o A169630 a169630 n = a007598 n * n -- _Reinhard Zumkeller_, Sep 01 2013
%o A169630 (PARI) vector(40, n, n--; n*fibonacci(n)^2) \\ _Michel Marcus_, Jul 09 2015
%Y A169630 Cf. A000045, A007598, A045925, A282464 (partial sums).
%K A169630 nonn,easy
%O A169630 0,3
%A A169630 _R. J. Mathar_, Mar 13 2010