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1, 3, 14, 36, 47, 246, 644, 843, 4414, 11556, 15127, 79206, 207364, 271443, 1421294, 3720996, 4870847, 25504086, 66770564, 87403803, 457652254, 1198149156, 1568397607, 8212236486, 21499914244, 28143753123, 147362604494
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 18*a(n-3)-a(n-6) for n>6. G.f.: -(3*x^6+6*x^5+7*x^4-18*x^3-14*x^2-3*x-1) / ((x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)). - Colin Barker, Jun 27 2013
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MAPLE
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with(GraphTheory): nmax:=116; P:=9: G:=PathGraph(P): A:= AdjacencyMatrix(G): for n from 0 to nmax do B(n):=A^n; A178381(n):=add(B(n)[1, k], k=1..P); od: for n from 0 to nmax-1 do a(n):= denom(A178381(4*n+1)/A178381(4*n)) od: seq(a(n), n=0..nmax/4-1);
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MATHEMATICA
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LinearRecurrence[{0, 0, 18, 0, 0, -1}, {1, 3, 14, 36, 47, 246, 644}, 30] (* Harvey P. Dale, Jun 11 2022 *)
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CROSSREFS
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KEYWORD
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easy,frac,nonn
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AUTHOR
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STATUS
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approved
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