A369836 Number of compositions of 5*n into parts 1 and 5.

1, 2, 8, 34, 140, 571, 2328, 9496, 38740, 158045, 644761, 2630364, 10730820, 43777405, 178594110, 728591751, 2972359720, 12126025705, 49469281395, 201814663875, 823322219501, 3358821723401, 13702634402876, 55901207340276, 228054320813276, 930369409108152

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-10,10,-5,1).

Formula

a(n) = A003520(5*n).

a(n) = Sum_{k=0..n} binomial(n+4*k,n-k).

a(n) = 6*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: (1-x)^4/((1-x)^5 - x).

Mathematica

LinearRecurrence[{6, -10, 10, -5, 1}, {1, 2, 8, 34, 140}, 50] (* Paolo Xausa, Mar 15 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+4*k, n-k));

Crossrefs

Cf. A079675, A369837, A369838, A369839.

Cf. A099131, A369840, A369845.

Cf. A003520.

Sequence in context: A000163 A117616 A345757 * A228655 A192402 A014445

Adjacent sequences: A369833 A369834 A369835 * A369837 A369838 A369839

Keyword

nonn

Author

Seiichi Manyama, Feb 03 2024

Status

approved