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 A099622 Sum C(n-k,k-1)4^(n-k-1)(5/4)^k, k=0..floor(n/2). 1
 0, 1, 8, 53, 316, 1785, 9744, 51997, 273092, 1417889, 7299160, 37334661, 190028748, 963565513, 4871514656, 24572321645, 123720601684, 622038982257, 3123938806632, 15674669614549, 78593250398300, 393845861293721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS In general a(n)=sum{k=0..floor(n/2),C(n-k,k+1)u^(n-k-1)(v/u)^(k-1)} has g.f. x^2/((1-u*x)(1-u*x-v*x^2)) and satisfies the recurrence a(n)=2u*a(n-1)-(u^2-v)a(n-2)-u*v*a(n-3). LINKS Index entries for linear recurrences with constant coefficients, signature (8,-11,-20). FORMULA G.f.: x^2/((1-4x)(1-4x-5x^2)); a(n)=8a(n-1)-11a(n-2)-20a(n-3). MATHEMATICA LinearRecurrence[{8, -11, -20}, {0, 1, 8}, 30] (* Harvey P. Dale, Nov 05 2017 *) CROSSREFS Cf. A094705, A099621. Sequence in context: A316424 A317426 A212754 * A198846 A291662 A110099 Adjacent sequences:  A099619 A099620 A099621 * A099623 A099624 A099625 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 25 2004 STATUS approved

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Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)