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A083880
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a(0)=1, a(1)=5, a(n) = 10*a(n-1) - 23*a(n-2), n >= 2.
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4
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1, 5, 27, 155, 929, 5725, 35883, 227155, 1446241, 9237845, 59114907, 378678635, 2427143489, 15561826285, 99793962603, 640017621475, 4104915074881, 26328745454885, 168874407826587, 1083182932803515, 6947717948023649
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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.: (1-5x)/(1-10x+23x^2).
E.g.f.: exp(5x)cosh(x*sqrt(2)).
a(n) = ((5-sqrt(2))^n + (5+sqrt(2))^n)/2;
a(n) = Sum_{k=0..n} C(n, 2k)*5^(n-2k)*2^k.
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MATHEMATICA
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LinearRecurrence[{10, -23}, {1, 5}, 30] (* Harvey P. Dale, May 14 2018 *)
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PROG
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(PARI) a(n)=if(n<0, 0, polsym(23-10*x+x^2, n)[n+1]/2)
(Magma) [ n eq 1 select 1 else n eq 2 select 5 else 10*Self(n-1)-23*Self(n-2): n in [1..21] ]; // Klaus Brockhaus, Dec 16 2008
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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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EXTENSIONS
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STATUS
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approved
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