A346077 -id:A346077 - cp's OEIS frontend

A346075 a(n) = 1 + Sum_{k=1..n-3} a(k) * a(n-k-3).

1, 1, 1, 1, 2, 3, 4, 6, 10, 16, 25, 41, 69, 115, 192, 326, 558, 955, 1641, 2839, 4930, 8578, 14972, 26222, 46037, 80988, 142793, 252307, 446617, 791885, 1406394, 2501642, 4456080, 7947963, 14194221, 25379751, 45430710, 81409233, 146028788, 262192876, 471193406

Offset: 0

Ilya Gutkovskiy, Jul 04 2021

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A105633, A216604, A217282, A307970, A343304, A346047, A346076, A346077.

a[n_] := a[n] = 1 + Sum[a[k] a[n - k - 3], {k, 1, n - 3}]; Table[a[n], {n, 0, 40}]
nmax = 40; A[] = 0; Do[A[x] = 1/(1 - x) + x^3 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

@CachedFunction
def a(n): # a = A346075
    if (n<4): return 1
    else: return 1 + sum(a(k)*a(n-k-3) for k in range(1,n-2))
[a(n) for n in range(51)] # G. C. Greubel, Nov 27 2022

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

A346076 a(n) = 1 + Sum_{k=1..n-4} a(k) * a(n-k-4).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 11, 17, 25, 36, 54, 84, 131, 201, 307, 475, 745, 1172, 1837, 2878, 4531, 7173, 11381, 18057, 28669, 45624, 72796, 116336, 186066, 297865, 477505, 766621, 1232214, 1982292, 3191693, 5143974, 8298640, 13399691, 21652705, 35014373, 56663700

Offset: 0

Ilya Gutkovskiy, Jul 04 2021

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A105633, A217282, A307971, A343305, A346048, A346073, A346075, A346077.

a[n_] := a[n] = 1 + Sum[a[k] a[n - k - 4], {k, 1, n - 4}]; Table[a[n], {n, 0, 44}]
nmax = 44; A[] = 0; Do[A[x] = 1/(1 - x) + x^4 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

@CachedFunction
def a(n): # a = A346076
    if (n<5): return 1
    else: return 1 + sum(a(k)*a(n-k-4) for k in range(1,n-3))
[a(n) for n in range(51)] # G. C. Greubel, Nov 27 2022

G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x^4 * A(x) * (A(x) - 1).

cp's OEIS Frontend

A346075 a(n) = 1 + Sum_{k=1..n-3} a(k) * a(n-k-3).

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