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A173497 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2), starting 2,1. 3
2, 1, 2, 3, 4, 6, 8, 11, 15, 21, 29, 40, 55, 75, 103, 141, 193, 264, 361, 493, 674, 921, 1258, 1719, 2348, 3208, 4382, 5986, 8177, 11170, 15259, 20844, 28474, 38896, 53133, 72581, 99148, 135439, 185013, 252733, 345240, 471607, 644227, 880031 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The limiting ratio is a(n+1)/a(n): 1.36602540378443.

This limiting ratio is (1+sqrt(3))/2. - Robert Israel, Aug 30 2020

LINKS

Robert Israel, Table of n, a(n) for n = 0..7374

FORMULA

a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2).

MAPLE

A[0]:= 2: A[1]:= 1:

for n from 2 to 100 do

  A[n]:= A[n-1]+A[n-2]-floor(A[n-2]/2)

od:

seq(A[i], i=0..100); # Robert Israel, Aug 30 2020

MATHEMATICA

l[0] = 2; l[1] = 1;

l[n_] := l[n] = l[n - 1] + l[n - 2] - Floor[l[n - 2]/2]

Table[l[n], {n, 0, 30}]

RecurrenceTable[{a[0]==2, a[1]==1, a[n]==a[n-1]+a[n-2]-Floor[a[n-2]/2]}, a, {n, 50}] (* Harvey P. Dale, Apr 26 2016 *)

CROSSREFS

Cf. A064323, A000032.

Sequence in context: A277282 A191973 A290973 * A022875 A325841 A076480

Adjacent sequences:  A173494 A173495 A173496 * A173498 A173499 A173500

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Nov 23 2010

EXTENSIONS

More terms from Max Alekseyev, Jun 18 2011

STATUS

approved

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Last modified September 18 10:13 EDT 2021. Contains 347518 sequences. (Running on oeis4.)