A114849 F(4n+4)/F(4)-F(3n+3)/F(3) where F(n)=A000045(n).

0, 3, 31, 257, 1950, 14164, 100464, 702919, 4878575, 33695365, 232040622, 1595043816, 10952137040, 75149854091, 515435467055, 3534332855753, 24230970910510, 166108203507452, 1138635489987488, 7804802111777935

Offset

0,2

Comments

The limit as n -> infinity of a(n+1)/a(n) is (1+sqrt(5))*(2+sqrt(5))/2 = 6.8541019662...

Old name was: Difference between two Fibonacci cycles A000045 (three's cycle minus two's cycle).

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (11,-28,-3,1)

Formula

a(n) = F(4n+4)/F(4)-F(3n+3)/F(3) = (2*F(4n+4)-3*F(3n+3))/6, where F=A000045.

G.f.: x*(2*x-3) / ((x^2-7*x+1)*(x^2+4*x-1)). - Colin Barker, Mar 15 2013

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] b = Table[a[4*(n + 1)]/a[4], {n, 0, 25}]; c = Table[a[3*(n + 1)]/a[3], {n, 0, 25}]; aout = b - c
LinearRecurrence[{11, -28, -3, 1}, {0, 3, 31, 257}, 20] (* Harvey P. Dale, Jun 09 2022 *)

Crossrefs

Cf. A000045.

Sequence in context: A057972 A221821 A198852 * A221899 A242134 A221894

Adjacent sequences: A114846 A114847 A114848 * A114850 A114851 A114852

Keyword

nonn,easy

Author

Roger L. Bagula, Feb 20 2006

Extensions

Edited by Bruno Berselli, Mar 15 2013

Put formula as clearer name, Joerg Arndt, Mar 15 2013

Status

approved