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A369845
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Number of compositions of 5*n into parts 3 and 5.
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7
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1, 1, 1, 2, 7, 22, 58, 138, 319, 750, 1810, 4427, 10828, 26349, 63862, 154603, 374521, 908140, 2203162, 5344988, 12964858, 31443013, 76253683, 184929945, 448506736, 1087774536, 2638209313, 6398479259, 15518219326, 37636240539, 91279009255, 221378866489
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/3)} binomial(n+2*k,n-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.: (1-x)^4/((1-x)^5 - x^3).
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MATHEMATICA
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LinearRecurrence[{5, -10, 11, -5, 1}, {1, 1, 1, 2, 7}, 50] (* Paolo Xausa, Mar 15 2024 *)
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PROG
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(PARI) a(n) = sum(k=0, n\3, binomial(n+2*k, n-3*k));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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