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
Keywords
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).
Programs
-
Mathematica
LinearRecurrence[{6, -10, 10, -5, 1}, {1, 2, 8, 34, 140}, 50] (* Paolo Xausa, Mar 15 2024 *) -
PARI
a(n) = sum(k=0, n, binomial(n+4*k, n-k));
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).