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A285187
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a(n) = Sum(psi(k-1)*psi(n-k-1),k=0..n)+(1-(-1)^n)/2, where psi(k) = A000931(k+6).
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0
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1, 3, 3, 7, 9, 15, 22, 33, 48, 71, 101, 147, 208, 297, 419, 591, 829, 1161, 1619, 2255, 3130, 4339, 6000, 8285, 11419, 15717, 21600, 29649, 40645, 55659, 76135, 104043, 142045, 193759, 264078, 359637, 489408, 665539, 904449, 1228343, 1667216, 2261593, 3066183
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 + 3*x - 4*x^3 - 3*x^4 + x^5 + 2*x^6 + x^7) / ((1 - x)*(1 + x)*(1 - x^2 - x^3)^2).
a(n) = 3*a(n-2) + 2*a(n-3) - 3*a(n-4) - 4*a(n-5) + 2*a(n-7) + a(n-8) for n>7. (End)
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MAPLE
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A000931 := proc(n) option remember; if n = 0 then 1 elif n <= 2 then 0 else procname(n-2)+procname(n-3); fi; end;
f:=n->add(psi(k-1)*psi(n-k-1), k=0..n)+(1-(-1)^n)/2;
[seq(f(n), n=0..40)];
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MATHEMATICA
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b[n_] := b[n] = Which[n == 0, 1, n <= 2, 0, True, b[n-2] + b[n-3]];
psi[n_] := b[n+6];
a[n_] := Sum[psi[k-1]*psi[n-k-1], {k, 0, n}] + (1-(-1)^n)/2;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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