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A033192 a(n) = binomial(Fibonacci(n) + 1, 2). 9
0, 1, 1, 3, 6, 15, 36, 91, 231, 595, 1540, 4005, 10440, 27261, 71253, 186355, 487578, 1276003, 3339820, 8742471, 22885995, 59912931, 156848616, 410626153, 1075018896, 2814412825, 7368190921, 19290113571, 50502074766, 132215989335, 346145696820, 906220783315 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is the sum of n-th row in Wythoff array A003603. [Reinhard Zumkeller, Jan 26 2012]

A subsequence of the triangular numbers A000217. In fact, binomial(F(n)+1,2) = A000217(F(n)). - M. F. Hasler, Jan 27 2012

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2394

James P. Jones, Péter Kiss, Representation of integers as terms of a linear recurrence with maximal index, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae, 25. (1998) pp. 21-37. See Theorem 3.7 p. 33.

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

FORMULA

G.f.: x(x^3-x^2-2x+1)/[(1+x)(1-3x+x^2)(1-x-x^2)].

a(n) = ((Fibonacci(n)+Fibonacci(n)^2)/2). - Gary Detlefs Dec 24 2010

Equals A000217 o A000045. - M. F. Hasler, Jan 27 2012

a(n) = A032441(n) - 1. - Filip Zaludek, Oct 30 2016

MAPLE

a:= n-> (f-> f*(f+1)/2)((<<0|1>, <1|1>>^n)[1, 2]):

seq(a(n), n=0..35); # Alois P. Heinz, Sep 06 2008

MATHEMATICA

Table[Binomial[Fibonacci[n] + 1, 2], {n, 0, 50}] (* Alonso del Arte, Jan 26 2012 *)

LinearRecurrence[{3, 1, -5, -1, 1}, {0, 1, 1, 3, 6}, 40] (* Harvey P. Dale, Apr 04 2020 *)

PROG

(PARI) a(n)=binomial(fibonacci(n)+1, 2) \\ Charles R Greathouse IV, Jan 26 2012

CROSSREFS

Cf. A000045, A000217, A033191, A081667.

Sequence in context: A291013 A017924 A052827 * A174297 A005043 A099323

Adjacent sequences: A033189 A033190 A033191 * A033193 A033194 A033195

KEYWORD

nonn,easy

AUTHOR

Simon P. Norton (simon(AT)dpmms.cam.ac.uk)

STATUS

approved

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Last modified December 5 05:50 EST 2022. Contains 358578 sequences. (Running on oeis4.)