A049674 a(n) = (F(3*n) - 2*F(n))/6, where F=A000045 (the Fibonacci sequence).

0, 0, 1, 5, 23, 100, 428, 1820, 7721, 32725, 138655, 587400, 2488344, 10540920, 44652257, 189150325, 801254167, 3394167980, 14377927684, 60905881300, 258001457065, 1092911716325, 4629648333311, 19611505067280

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