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A024551 a(n) = floor(a(n-1)/(sqrt(5) - 2)) for n > 0 and a(0) = 1. 3
1, 4, 16, 67, 283, 1198, 5074, 21493, 91045, 385672, 1633732, 6920599, 29316127, 124185106, 526056550, 2228411305, 9439701769, 39987218380, 169388575288, 717541519531, 3039554653411, 12875760133174, 54542595186106, 231046140877597 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..250

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

FORMULA

a(n) = 5*a(n-1) - 3*a(n-2) - a(n-3). - Clark Kimberling, Aug 16 2012

G.f.: (-x^2-x+1)/[(1-x)(1-4x-x^2)].

MATHEMATICA

a[0] = 1;

a[n_] := Floor[a[n - 1]/FractionalPart[Sqrt[5]]]

Table[a[n], {n, 0, 60}]

(* Clark Kimberling, Aug 16 2012 *)

a[0]=1;

a[1]=4;

a[2]=16;

a[n_]:=Floor[a[n-1]^2/a[n-2]]+3

Table[a[n], {n, 0, 60}]

PROG

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, -3, 5]^n*[1; 4; 16])[1, 1] \\ Charles R Greathouse IV, Jan 20 2017

(PARI) step(n)=2*n + sqrtint(5*n^2)

a(n)=if(n, step(a(n-1)), 1) \\ Charles R Greathouse IV, Jan 20 2017

CROSSREFS

Sequence in context: A218645 A273582 A183275 * A261048 A091153 A270765

Adjacent sequences:  A024548 A024549 A024550 * A024552 A024553 A024554

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 24 11:06 EST 2018. Contains 299603 sequences. (Running on oeis4.)