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 A099504 Expansion of 1/(1-5*x+x^3). 5
 1, 5, 25, 124, 615, 3050, 15126, 75015, 372025, 1844999, 9149980, 45377875, 225044376, 1116071900, 5534981625, 27449863749, 136133246845, 675131252600, 3348206399251, 16604898749410, 82349362494450, 408398606072999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A transform of A000351 under the mapping g(x)->(1/(1+x^3))g(x/(1+x^3)). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,0,-1). FORMULA a(n) = 5*a(n-1) - a(n-3). a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k, k)*(-1)^k*5^(n-3*k). MAPLE A099504:=n->sum(binomial(n-2*i, i)*(-1)^i*5^(n-3*i), i=0..floor(n/3)); seq(A099504(n), n=0..30); # Wesley Ivan Hurt, Dec 03 2013 MATHEMATICA Table[Sum[Binomial[n-2*i, i]*(-1)^i*5^(n-3*i), {i, 0, Floor[n/3]}], {n, 0, 30}] (* Wesley Ivan Hurt, Dec 03 2013 *) LinearRecurrence[{5, 0, -1}, {1, 5, 25}, 30] (* G. C. Greubel, Aug 03 2023 *) PROG (Magma) [n le 3 select 5^(n-1) else 5*Self(n-1) -Self(n-3): n in [1..30]]; // G. C. Greubel, Aug 03 2023 (SageMath) @CachedFunction def a(n): # a = A099504 if (n<3): return 5^n else: return 5*a(n-1) - a(n-3) [a(n) for n in range(31)] # G. C. Greubel, Aug 03 2023 CROSSREFS Cf. A000071, A000351, A076264, A099503. Sequence in context: A086093 A171279 A231636 * A299958 A036156 A097756 Adjacent sequences: A099501 A099502 A099503 * A099505 A099506 A099507 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 20 2004 STATUS approved

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Last modified October 4 19:37 EDT 2023. Contains 365888 sequences. (Running on oeis4.)