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A369847
Number of compositions of 5*n-2 into parts 3 and 5.
5
1, 2, 3, 5, 12, 34, 92, 230, 549, 1299, 3109, 7536, 18364, 44713, 108575, 263178, 637699, 1545839, 3749001, 9093989, 22058847, 53501860, 129755543, 314685488, 763192224, 1850966760, 4489176073, 10887655332, 26405874658, 64042115197, 155321124452
OFFSET
1,2
FORMULA
a(n) = A052920(5*n-2).
a(n) = Sum_{k=0..floor(n/3)} binomial(n+2*k,n-1-3*k).
a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x*(1-x)^3/((1-x)^5 - x^3).
MATHEMATICA
LinearRecurrence[{5, -10, 11, -5, 1}, {1, 2, 3, 5, 12}, 50] (* Paolo Xausa, Mar 15 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n+2*k, n-1-3*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 03 2024
STATUS
approved