A182230 a(n) = a(n-1)+floor(a(n-2)/4) with a(0)=3, a(1)=4.

3, 4, 4, 5, 6, 7, 8, 9, 11, 13, 15, 18, 21, 25, 30, 36, 43, 52, 62, 75, 90, 108, 130, 157, 189, 228, 275, 332, 400, 483, 583, 703, 848, 1023, 1235, 1490, 1798, 2170, 2619, 3161, 3815, 4605, 5558, 6709, 8098, 9775, 11799, 14242, 17191, 20751, 25048, 30235

Offset: 0

Author

Alex Ratushnyak, Apr 19 2012

Keywords

• nonn

Comments

a(n)/a(n-1) tends to (1+sqrt(2))/2 = 1.207106781186547524... [Bruno Berselli, Apr 23 2012]

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A064323, A064324, A182229, A182280; A174968.

Programs

Haskell

a182230 n = a182230_list !! n
a182230_list = 3 : 4 : zipWith (+)
                       (map (flip div 4) a182230_list) (tail a182230_list)
-- Reinhard Zumkeller, Apr 30 2015

Magma

[n le 2 select n+2 else Self(n-1)+Floor(Self(n-2)/4): n in [1..52]]; // Bruno Berselli, Apr 20 2012

Maple

a:= proc(n) a(n):= a(n-1) +floor(a(n-2)/4) end: a(0), a(1):= 3, 4:
seq(a(n), n=0..60);  # Alois P. Heinz, Apr 20 2012

Mathematica

RecurrenceTable[{a[0] == 3, a[1] == 4, a[n] == a[n - 1] + Floor[a[n - 2]/4]}, a, {n, 51}] (* Bruno Berselli, Apr 21 2012 *)

Python

prpr = 3
prev = 4
for i in range(2,55):
    current = prev + prpr//4
    print(current, end=',')
    prpr = prev
    prev = current