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 A115730 a(n) = a(n-3)+A001654(n-1) with a(0)=0, a(1)=0 and a(2)=1. 5
 0, 0, 1, 2, 6, 16, 42, 110, 289, 756, 1980, 5184, 13572, 35532, 93025, 243542, 637602, 1669264, 4370190, 11441306, 29953729, 78419880, 205305912, 537497856, 1407187656, 3684065112, 9645007681, 25250957930, 66107866110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Old name was: Dihedral D2 elliptical invariant transform on A000045: a[n+1]/a[n]= 1+Phi=1+(1+Sqrt[5])/2. The a(n+1) represent the Ca2 and Ze4 sums of the Golden Triangle A180662. Furthermore the a(3*n) represent the Ze1 (terms doubled) and Ca3 sums of the Golden triangle. See A180662 for more information about these and other triangle sums. LINKS Index entries for linear recurrences with constant coefficients, signature (2,2,0,-2,-2,1). FORMULA a(n) = -Floor[g[b[n+1]] where b[n]=A000045[n], g[x]=(x^2-1)^2/(-4*x^2). G.f.: -x^2 / ( (x-1)*(1+x)*(1+x+x^2)*(x^2-3*x+1) ). - R. J. Mathar, Jun 20 2015 a(n)-a(n-2) = A182890(n-1). - R. J. Mathar, Jun 20 2015 MAPLE nmax:=31: with(combinat): for n from 0 to nmax do A001654(n):=fibonacci(n) * fibonacci(n+1) od: a(0):=0: a(1):=0: a(2):=1: for n from 3 to nmax do a(n):=a(n-3) + A001654(n-1) od: seq(a(n), n=0..nmax); MATHEMATICA F[0] = 0; F[1] = 1; F[n_] := F[n] = F[n - 1] + F[n - 2] g[x_] = (x^2 - 1)^2/(-4*x^2) a = Table[ -Floor[g[F[n]]], {n, 1, 32}] Table[N[a[[n + 1]]/a[[n]]], {n, 1, Length[a] - 1}] CROSSREFS Cf. A001654, A000045, A079962, A064831, A180664, A180665, A180666. Sequence in context: A156664 A025169 A111282 * A191694 A224232 A217661 Adjacent sequences:  A115727 A115728 A115729 * A115731 A115732 A115733 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Mar 13 2006 EXTENSIONS Corrected and information added by Johannes W. Meijer, Sep 22 2010 Edited by Editors-in-Chief. - N. J. A. Sloane, Jun 20 2015 STATUS approved

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Last modified January 21 08:09 EST 2020. Contains 331104 sequences. (Running on oeis4.)