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 A049674 a(n) = (F(3*n) - 2*F(n))/6, where F=A000045 (the Fibonacci sequence). 1
 0, 0, 1, 5, 23, 100, 428, 1820, 7721, 32725, 138655, 587400, 2488344, 10540920, 44652257, 189150325, 801254167, 3394167980, 14377927684, 60905881300, 258001457065, 1092911716325, 4629648333311, 19611505067280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-2,-5,-1). FORMULA From L. Edson Jeffery, Oct 06 2012: (Start) G.f.: x^2/(1-5x+2x^2+5x^3+x^4). [Corrected by Georg Fischer, May 18 2019] a(n) = 5*a(n-1) - 2*a(n-2) - 5*a(n-3) - a(n-4), n>=4, a(0)=a(1)=0, a(2)=1, a(3)=5. (End) a(n) = Sum_{k=0..n} F(3*k)*F(n-k)/2, for F(n) = A000045(n), the Fibonacci sequence. - Greg Dresden, Aug 27 2021 MATHEMATICA LinearRecurrence[{5, -2, -5, -1}, {0, 0, 1, 5}, 50] (* or *) Table[( Fibonacci[3*n] - 2*Fibonacci[n])/6, {n, 0, 30}] (* G. C. Greubel, Dec 02 2017 *) PROG (PARI) for(n=0, 30, print1((fibonacci(3*n) - 2*fibonacci(n))/6, ", ")) \\ G. C. Greubel, Dec 02 2017 (Magma) [(Fibonacci(3*n) - 2*Fibonacci(n))/6: n in [0..30]]; // G. C. Greubel, Dec 02 2017 CROSSREFS Cf. A000045. Sequence in context: A364754 A339232 A196489 * A077277 A073682 A034958 Adjacent sequences: A049671 A049672 A049673 * A049675 A049676 A049677 KEYWORD nonn,easy AUTHOR Clark Kimberling STATUS approved

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Last modified May 22 10:24 EDT 2024. Contains 372745 sequences. (Running on oeis4.)