OFFSET
0,2
COMMENTS
a(n)/a(n-1) approaches (1+sqrt(3))/2 = 1.3660254... = A332133 for large n.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..400
FORMULA
a(n) = A064323(n) + 1.
EXAMPLE
a(5) = a(4)+floor(a(3)/2) = 4+floor(3/2) = 5.
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 *)
PROG
(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
(Magma) [n le 2 select n else Self(n-1)+Floor(Self(n-2)/2): n in [1..45]]; // Bruno Berselli, Apr 20 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Sep 11 2001
STATUS
approved