A369851 Number of compositions of 5*n-3 into parts 4 and 5.
0, 0, 1, 4, 10, 20, 36, 65, 129, 285, 661, 1521, 3394, 7359, 15706, 33457, 71760, 155248, 337745, 735723, 1600062, 3471298, 7517368, 16269333, 35221440, 76302420, 165392856, 358594516, 777451793, 1685254125, 3652428851, 7915135727, 17152718719, 37172960128
Offset: 1
Links
- Paolo Xausa, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-4,1).
Programs
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Mathematica
LinearRecurrence[{5, -10, 10, -4, 1}, {0, 0, 1, 4, 10}, 50] (* Paolo Xausa, Mar 15 2024 *) -
PARI
a(n) = sum(k=0, n\4, binomial(n+k, n-3-4*k));
Formula
a(n) = A017827(5*n-3).
a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,n-3-4*k).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 4*a(n-4) + a(n-5).
G.f.: x^3*(1-x)/((1-x)^5 - x^4).