A393182 G.f. A(x) satisfies: A(x) = 1 + x^2 + x^3 * A(x)^2 / (1 - x).

1, 0, 1, 1, 1, 3, 5, 8, 16, 29, 53, 102, 192, 365, 705, 1358, 2632, 5134, 10032, 19682, 38754, 76487, 151389, 300400, 597350, 1190402, 2376896, 4754454, 9526538, 19118747, 38426161, 77340080, 155867134, 314516682, 635394816, 1285068958

Offset

0,6

Links

Table of n, a(n) for n=0..35.

Formula

G.f.: (1 - x - sqrt((1 - x) * (1 - x - 4*x^3 - 4*x^5))) / (2*x^3).

a(0) = 1, a(1) = 0, a(2) = 1; a(n) = Sum_{j=0..n-3} Sum_{i=0..j} a(i) * a(j-i).

Mathematica

nmax = 35; A[_] = 0; Do[A[x_] = 1 + x^2 + x^3 A[x]^2/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 35; CoefficientList[Series[(1 - x - Sqrt[(1 - x) (1 - x - 4 x^3 - 4 x^5)])/(2 x^3), {x, 0, nmax}], x]
a[0] = 1; a[1] = 0; a[2] = 1; a[n_] := a[n] = Sum[Sum[a[i] a[j - i], {i, 0, j}], {j, 0, n - 3}]; Table[a[n], {n, 0, 35}]

Crossrefs

Cf. A002212, A023431, A090345, A346503, A346504, A357307, A393181.

Sequence in context: A056765 A380797 A080006 * A374680 A174011 A291223

Adjacent sequences: A393179 A393180 A393181 * A393183 A393184 A393185

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2026

Status

approved