A369849 Number of compositions of 5*n-1 into parts 4 and 5.
1, 2, 3, 4, 6, 13, 35, 92, 220, 484, 1013, 2092, 4382, 9404, 20552, 45185, 99009, 215481, 466361, 1006897, 2174834, 4705895, 10200142, 22128873, 48009456, 104111224, 225655617, 488945055, 1059372394, 2295532150, 4974876116, 10782658417, 23371307904, 50655960304
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}, {1, 2, 3, 4, 6}, 50] (* Paolo Xausa, Mar 15 2024 *) -
PARI
a(n) = sum(k=0, n\4, binomial(n+k, n-1-4*k));
Formula
a(n) = A017827(5*n-1).
a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,n-1-4*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*(1-x)^3/((1-x)^5 - x^4).