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A097790
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a(n)=5a(n-1)+C(n+3,3),n>0, a(0)=1.
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2
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1, 9, 55, 295, 1510, 7606, 38114, 190690, 953615, 4768295, 23841761, 119209169, 596046300, 2980232060, 14901160980, 74505805716, 372529029549, 1862645148885, 9313225745755, 46566128730315, 232830643653346
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f. : 1/((1-5x)(1-x)^4)); a(n)=5^(n+4)/256-(32n^3+312n^2+1012n+1107)/768; a(n)=sum{k=0..n, binomial(n+4, k+4)4^k }.
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, 5a+Binomial[n+4, 3]}; NestList[nxt, {0, 1}, 20][[All, 2]] (* or *) LinearRecurrence[{9, -26, 34, -21, 5}, {1, 9, 55, 295, 1510}, 30] (* Harvey P. Dale, Sep 20 2022 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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