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A369842
Number of compositions of 5*n-1 into parts 2 and 5.
5
1, 3, 7, 18, 52, 154, 450, 1301, 3753, 10838, 31327, 90568, 261813, 756786, 2187496, 6323023, 18277014, 52830706, 152709940, 441415867, 1275934888, 3688154521, 10660798289, 30815580241, 89074003241, 257472939209, 744238632362, 2151259638423, 6218325456983
OFFSET
1,2
FORMULA
a(n) = A001687(5*n).
a(n) = Sum_{k=0..floor(n/2)} binomial(n+1+3*k,n-1-2*k).
a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x*(1-x)^2/((1-x)^5 - x^2).
MATHEMATICA
LinearRecurrence[{5, -9, 10, -5, 1}, {1, 3, 7, 18, 52}, 50] (* Paolo Xausa, Mar 15 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(n+1+3*k, n-1-2*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved