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A369848
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Number of compositions of 5*n-4 into parts 3 and 5.
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5
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0, 1, 3, 6, 11, 23, 57, 149, 379, 928, 2227, 5336, 12872, 31236, 75949, 184524, 447702, 1085401, 2631240, 6380241, 15474230, 37533077, 91034937, 220790480, 535475968, 1298668192, 3149634952, 7638811025, 18526466357, 44932341015, 108974456212, 264295580664
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OFFSET
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1,3
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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-2-3*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^2*(1-x)^2/((1-x)^5 - x^3).
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MATHEMATICA
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LinearRecurrence[{5, -10, 11, -5, 1}, {0, 1, 3, 6, 11}, 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-2-3*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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