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A369843
Number of compositions of 5*n-3 into parts 2 and 5.
5
1, 2, 4, 11, 34, 102, 296, 851, 2452, 7085, 20489, 59241, 171245, 494973, 1430710, 4135527, 11953991, 34553692, 99879234, 288705927, 834519021, 2412219633, 6972643768, 20154781952, 58258423000, 168398935968, 486765693153, 1407021006061, 4067065818560
OFFSET
1,2
FORMULA
a(n) = A001687(5*n-2).
a(n) = Sum_{k=0..floor(n/2)} binomial(n+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)^3/((1-x)^5 - x^2).
MATHEMATICA
LinearRecurrence[{5, -9, 10, -5, 1}, {1, 2, 4, 11, 34}, 50] (* Paolo Xausa, Mar 15 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\2, binomial(n+3*k, n-1-2*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved