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A073374
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Fourth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.
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3
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1, 5, 25, 95, 340, 1106, 3430, 10130, 28915, 80035, 216143, 571225, 1482110, 3783640, 9522740, 23665300, 58149845, 141435985, 340854645, 814589475, 1931900376, 4549699950, 10645737330, 24761578470
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (5,0,-30,15,81,-30,-120,0,80,32).
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FORMULA
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a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073373(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+4, 4) * binomial(n-k, k) * 2^k.
a(n) = (5*(2968 +1974*n +411*n^2 +27*n^3)*(n+1)*U(n+1) + 2*(9412 +6099*n +1248*n^2 +81*n^3)*(n+2)*U(n))/(4!*3^7) with U(n) = A001045(n+1), n>=0.
G.f.: 1/(1-(1+2*x)*x)^5 = 1/((1+x)*(1-2*x))^5.
E.g.f.: (1/157464)*(512*(263 + 1104*x + 1026*x^2 + 306*x^3 + 27*x^4)*exp(2*x) + (22808 - 24432*x + 7344*x^2 - 792*x^3 + 27*x^4)*exp(-x)). - G. C. Greubel, Sep 29 2022
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MATHEMATICA
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Table[(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464, {n, 0, 40}] (* G. C. Greubel, Sep 29 2022 *)
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PROG
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(Magma) [(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464: n in [0..40]]; // G. C. Greubel, Sep 29 2022
(SageMath)
def A073374(n): return (2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464
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CROSSREFS
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Fifth (m=4) column of triangle A073370.
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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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