A064324 a(n) = a(n-1) + floor(a(n-2)/2) with a(0)=1, a(1)=2.

1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 22, 30, 41, 56, 76, 104, 142, 194, 265, 362, 494, 675, 922, 1259, 1720, 2349, 3209, 4383, 5987, 8178, 11171, 15260, 20845, 28475, 38897, 53134, 72582, 99149, 135440, 185014, 252734, 345241, 471608, 644228, 880032

Offset: 0

Author

Henry Bottomley, Sep 11 2001

Keywords

• nonn

Comments

a(n)/a(n-1) approaches (1+sqrt(3))/2 = 1.3660254... = A332133 for large n.

Examples

			a(5) = a(4)+floor(a(3)/2) = 4+floor(3/2) = 5.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A064323, A332133, A182229, A182230.

Programs

Magma

[n le 2 select n else Self(n-1)+Floor(Self(n-2)/2): n in [1..45]]; // Bruno Berselli, Apr 20 2012

Mathematica

RecurrenceTable[{a[n] == a[n-1] + Floor[a[n-2]/2], a[0] == 1, a[1] == 2}, a, {n, 0, 50}] (* G. C. Greubel, May 04 2019 *)
nxt[{a_,b_}]:={b,Floor[a/2]+b}; NestList[nxt,{1,2},50][[;;,1]] (* Harvey P. Dale, Jul 28 2023 *)

PARI

{ for (n=0, 400, if (n>1, a=a1 + a2\2; a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); write("b064324.txt", n, " ", a) ) }; \\ Harry J. Smith, Sep 11 2009

Formula

a(n) = A064323(n) + 1.