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2, 4, 5, 26, 68, 89, 466, 1220, 1597, 8362, 21892, 28657, 150050, 392836, 514229, 2692538, 7049156, 9227465, 48315634, 126491972, 165580141, 866988874, 2269806340, 2971215073, 15557484098, 40730022148, 53316291173, 279167724890
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: -(x^5+4*x^4+10*x^3-5*x^2-4*x-2)/((x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)).
a(n) = 18*a(n-3)-a(n-6). (End)
a(3*n) = 2*Fibonacci(6*n+1),
a(3*n+1) = 2*Fibonacci(6*n+3),
a(3*n+2) = Fibonacci(6*n+5). (End)
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MAPLE
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with(GraphTheory): nmax:=120; 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+3)/A178381(4*n+2)) od: seq(a(n), n=0..nmax/4-1);
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MATHEMATICA
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Flatten[Table[{2*Fibonacci[6 n + 1], 2*Fibonacci[6 n + 3],
Fibonacci[6 n + 5]}, {n, 0, 10}]] (* Greg Dresden, Oct 16 2021 *)
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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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