A346047 -id:A346047 - cp's OEIS frontend

A346049 a(0) = ... = a(4) = 1; a(n) = Sum_{k=1..n-5} a(k) * a(n-k-5).

1, 1, 1, 1, 1, 0, 1, 2, 3, 4, 4, 4, 6, 10, 16, 24, 30, 37, 50, 74, 116, 175, 245, 332, 456, 654, 981, 1471, 2146, 3056, 4320, 6203, 9119, 13540, 19986, 29134, 42113, 61047, 89398, 132021, 195272, 287547, 421235, 616418, 905161, 1335648, 1976407, 2922982, 4313230

Offset: 0

Ilya Gutkovskiy, Jul 02 2021

nonn

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

Cf. A025250, A307972, A343305, A346047, A346048.

a[0] = a[1] = a[2] = a[3] = a[4] = 1; a[n_] := a[n] = Sum[a[k] a[n - k - 5], {k, 1, n - 5}]; Table[a[n], {n, 0, 48}]
nmax = 48; A[] = 0; Do[A[x] = 1 + x + x^2 + x^3 + x^4 + x^5 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

@CachedFunction
def a(n): # a = A346049
    if (n<5): return 1
    else: return sum(a(k)*a(n-k-5) for k in range(1,n-4))
[a(n) for n in range(51)] # G. C. Greubel, Nov 28 2022

G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 * A(x) * (A(x) - 1).

A346048 a(0) = ... = a(3) = 1; a(n) = Sum_{k=1..n-4} a(k) * a(n-k-4).

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 2, 3, 3, 3, 5, 9, 15, 19, 24, 35, 59, 95, 137, 191, 280, 445, 706, 1071, 1575, 2357, 3663, 5755, 8890, 13483, 20518, 31759, 49658, 77267, 119135, 183523, 284793, 444883, 694798, 1080865, 1679142, 2616399, 4092497, 6408249, 10021176, 15657643

Offset: 0

Ilya Gutkovskiy, Jul 02 2021

nonn

Cf. A025250, A307971, A343304, A343305, A346047, A346049.

a:= proc(n) option remember; `if`(n<4, 1,
      add(a(j)*a(n-4-j), j=1..n-4))
    end:
seq(a(n), n=0..45);  # Alois P. Heinz, Jul 03 2021

a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = Sum[a[k] a[n - k - 4], {k, 1, n - 4}]; Table[a[n], {n, 0, 45}]
nmax = 45; A[] = 0; Do[A[x] = 1 + x + x^2 + x^3 + x^4 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 * A(x) * (A(x) - 1).

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

Original entry on oeis.org

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).

cp's OEIS Frontend

A346049 a(0) = ... = a(4) = 1; a(n) = Sum_{k=1..n-5} a(k) * a(n-k-5).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

SageMath

Formula

A346048 a(0) = ... = a(3) = 1; a(n) = Sum_{k=1..n-4} a(k) * a(n-k-4).

Views

Author

Keywords

Crossrefs

Programs

Maple

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

SageMath

Formula