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A133641 a(n) = 2*L(n) + L(n-1) - n, L(n) = n-th Lucas number of A000032 starting (1,3,4,...). =. 0
1, 5, 8, 14, 24, 41, 69, 115, 190, 312, 510, 831, 1351, 2193, 3556, 5762, 9332, 15109, 24457, 39583, 64058, 103660, 167738, 271419, 439179, 710621, 1149824, 1860470, 3010320, 4870817, 7881165, 12752011, 20633206, 33385248, 54018486, 87403767, 141422287, 228826089, 370248412 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/a(n-1) tends to phi.

LINKS

Table of n, a(n) for n=1..39.

W. Kuszmaul, Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in Permutations, arXiv preprint arXiv:1509.08216 [cs.DM], 2015-2017.

FORMULA

Given n-th Lucas number of A000032 starting (1, 3, 4, 7,...), a(n) = 2*L(n) + L(n-1) - n.

G.f.: -x*(1-5*x^2+x^3+2*x+2*x^4)/(-1+x+x^2)/(-1+x)^2. - R. J. Mathar, Nov 14 2007

a(n) = A000032(n+2)-n = Fibonacci(n + 3) + Fibonacci(n + 1) - n, n>1. [R. J. Mathar, Jul 20 2009, extended by David A. Corneth, Aug 08 2018]

EXAMPLE

a(5) = 24 = 2*L(5) + L(4) - n = 2*11 + 7 - 5.

MATHEMATICA

a[1] = 1; a[n_] := LucasL[n+2] - n;

Array[a, 14] (* Jean-Fran├žois Alcover, Aug 08 2018, after R. J. Mathar *)

PROG

(PARI) a(n) = {if(n==1, 1, fibonacci(n+3)+fibonacci(n+1)-n)} \\ David A. Corneth, Aug 08 2018

CROSSREFS

Cf. A000032.

Sequence in context: A124011 A101835 A192522 * A164094 A246319 A302649

Adjacent sequences:  A133638 A133639 A133640 * A133642 A133643 A133644

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Sep 19 2007

STATUS

approved

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Last modified October 16 07:07 EDT 2021. Contains 348041 sequences. (Running on oeis4.)