A173497 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2), starting 2,1.

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

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 A350404 A325841

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