A167270 a(n) = Fibonacci(n + 2) + floor(n/2).

1, 2, 4, 6, 10, 15, 24, 37, 59, 93, 149, 238, 383, 616, 994, 1604, 2592, 4189, 6774, 10955, 17721, 28667, 46379, 75036, 121405, 196430, 317824, 514242, 832054, 1346283, 2178324, 3524593, 5702903, 9227481, 14930369, 24157834, 39088187, 63246004, 102334174, 165580160

Offset

0,2

Comments

a(n)/a(n-1) tends to phi, 1.6180339...; e.g. a(16)/a(15) = 2592/1604 = 1.6159...

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2, 1, -3, 0, 1)

Formula

G.f.: ( -1+x^3+x^2 ) / ( (1+x)*(x^2+x-1)*(x-1)^2 ). - R. J. Mathar, Mar 03 2013

a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) + a(n-5). - Andrew Howroyd, Aug 10 2018

Example

a(4) = 10 = (1 + 4 + 1 + 3 + 1).

Prog

(PARI) a(n) = fibonacci(n+2) + n\2; \\ Andrew Howroyd, Aug 10 2018
(PARI) Vec((1 - x^2 - x^3)/((1 - x)^2*(1 + x)*(1 - x - x^2)) + O(x^40)) \\ Andrew Howroyd, Aug 10 2018

Crossrefs

Row sums of A167269.

Sequence in context: A108925 A279026 A120549 * A355108 A060168 A113117

Adjacent sequences: A167267 A167268 A167269 * A167271 A167272 A167273

Keyword

nonn

Author

Gary W. Adamson & Mats Granvik, Oct 31 2009

Extensions

Name changed and terms a(17) and beyond from Andrew Howroyd, Aug 10 2018

Status

approved