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 A109537 a(0)=a(1)=a(2)=a(3)=a(4)=a(5)=1; a(n)=a(n-1)+a(n-2)-a(n-4)+a(n-6) for n>=6. 1
 1, 1, 1, 1, 1, 1, 2, 3, 5, 8, 12, 18, 27, 40, 60, 90, 135, 203, 305, 458, 688, 1033, 1551, 2329, 3497, 5251, 7885, 11840, 17779, 26697, 40088, 60196, 90390, 135729, 203810, 306040, 459548, 690055, 1036183, 1555927, 2336372, 3508284, 5268021, 7910433 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Limit[a(n)/a(n-1),n->Infinity]=1.50159 Thetas on a line are: {{0, 1.32472}, {1, 1.38028}, {2, 1.44327}, {3, 1.50159}} Using starting vector {1,1,1,1,1,1} vector Markov is: M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 0, -1, 0, 1, 1}} v[1] = {1, 1, 1, 1, 1, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}] LINKS FORMULA G.f.=(1-x^2-x^3)/(1-x-x^2+x^4-x^6). MAPLE a[0]:=1: a[1]:=1: a[2]:=1: a[3]:=1: a[4]:=1: a[5]:=1: for n from 6 to 45 do a[n]:=a[n-1]+a[n-2]-a[n-4]+a[n-6] od: seq(a[n], n=0..45); MATHEMATICA F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 1; F[5] = 1; F[6] = 1; F[n__] := F[n] = F[n - 1] + F[n - 2] - F[n - 4] + F[n - 6] aa = Table[F[n], {n, 1, 50}] CROSSREFS Sequence in context: A132842 A063978 A077868 * A081226 A156623 A061419 Adjacent sequences: A109534 A109535 A109536 * A109538 A109539 A109540 KEYWORD nonn AUTHOR Roger L. Bagula, Jun 19 2005 STATUS approved

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Last modified December 9 17:46 EST 2022. Contains 358703 sequences. (Running on oeis4.)