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A192727 a(n) = Fibonacci(n-2) + 2*a(n-2) - (n mod 2). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 1 03:52 EDT 2021. Contains 346384 sequences. (Running on oeis4.)