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

Author

Roger L. Bagula, Nov 23 2010

Keywords

• nonn

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

Crossrefs

Cf. A064323, A000032.

Programs

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 *)

Formula

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

Extensions

More terms from Max Alekseyev, Jun 18 2011