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A097113
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Expansion of (1+5x-12x^2-80x^3)/(1-33x^2+272x^4).
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0
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1, 5, 21, 85, 421, 1445, 8181, 24565, 155461, 417605, 2904981, 7099285, 53578981, 120687845, 977951541, 2051693365, 17698918021, 34878787205, 318061475541, 592939382485, 5681922991141, 10079969502245, 100990737360501
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: 5(1+x)/(1-17x^2)-4/(1-16x^2); a(n)=33a(n-2)-272a(n-4); a(n)=(5/2+5sqrt(17)/34)(sqrt(17))^n+(5/2-5sqrt(17)/34)(-sqrt(17))^n-4^(n+1)(1+(-1)^n)/2; a(n)=sum{k=0..n, binomial(floor(n/2), floor(k/2))4^k }.
a(0)=1, a(1)=5, a(2)=21, a(3)=85, a(n)=33*a(n-2)-272*a(n-4) [From Harvey P. Dale, Jul 19 2011]
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MATHEMATICA
| CoefficientList[Series[(1+5x-12x^2-80x^3)/(1-33x^2+272x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{0, 33, 0, -272}, {1, 5, 21, 85}, 30] (* From Harvey P. Dale, Jul 19 2011 *)
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CROSSREFS
| Sequence in context: A084241 A187063 A026855 * A012814 A039919 A010925
Adjacent sequences: A097110 A097111 A097112 * A097114 A097115 A097116
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 25 2004
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