A369839 Number of compositions of 5*n-4 into parts 1 and 5.
1, 3, 11, 45, 185, 756, 3084, 12580, 51320, 209365, 854126, 3484490, 14215310, 57992715, 236586825, 965178576, 3937538296, 16063564001, 65532845396, 267347509271, 1090669728772, 4449491452173, 18152125855049, 74053333195325, 302107654008601, 1232477063116753
Offset: 1
Links
- Paolo Xausa, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-10,10,-5,1).
Programs
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Mathematica
LinearRecurrence[{6, -10, 10, -5, 1}, {1, 3, 11, 45, 185}, 50] (* Paolo Xausa, Mar 15 2024 *) -
PARI
a(n) = sum(k=0, n, binomial(n+4*k, n-1-k));
Formula
a(n) = A003520(5*n-4).
a(n) = Sum_{k=0..n} binomial(n+4*k,n-1-k).
a(n) = 6*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x*(1-x)^3/((1-x)^5 - x).