A192727 a(n) = Fibonacci(n-2) + 2*a(n-2) - (n mod 2).

0, 0, 0, 0, 1, 1, 5, 6, 18, 24, 57, 81, 169, 250, 482, 732, 1341, 2073, 3669, 5742, 9922, 15664, 26609, 42273, 70929, 113202, 188226, 301428, 497845, 799273, 1313501, 2112774, 3459042, 5571816, 9096393, 14668209

Offset

0,7

Comments

The sequence is Fibonacci-like in the sense that a(n)/a(n-1) converges to the golden ratio as n goes to infinity.

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-5,2,2).

Formula

a(n) = Fibonacci(n-2) + 2*a(n-2) - n mod 2 for all n >= 2, with a(0) = a(1) = 0.

G.f.: -x^4 / ( (x-1)*(1+x)*(2*x^2-1)*(x^2+x-1) ). - R. J. Mathar, Jul 09 2011

a(n) = A000045(n+1) + A000035(n) - A016116(n+1). - R. J. Mathar, Jul 09 2011

Example

a(10) = is Fibonacci(8) + 2*a(8) - (10 mod 2) = 21 + 36 - 0 = 57.

Prog

(PARI) a(n) = if (n<=2, 0, fibonacci(n-2) + 2*a(n-2) - n % 2); \\ Michel Marcus, Aug 29 2013

Crossrefs

Sequence in context: A041555 A041747 A180134 * A056519 A295972 A333405

Adjacent sequences: A192724 A192725 A192726 * A192728 A192729 A192730

Keyword

nonn,easy

Author

Derek Devine, Jul 08 2011

Status

approved