A182229 -id:A182229 - cp's OEIS frontend

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

Henry Bottomley, Sep 11 2001

nonn

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

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

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

Cf. A064323, A332133, A182229, A182230.

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

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 *)

{ 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

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

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

Original entry on oeis.org

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

Alex Ratushnyak, Apr 19 2012

nonn

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

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

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

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

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

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

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 *)

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

A182281 a(n) = floor(a(n-1)/3)+a(n-2) with a(0)=2, a(1)=3.

Original entry on oeis.org

2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 11, 12, 15, 17, 20, 23, 27, 32, 37, 44, 51, 61, 71, 84, 99, 117, 138, 163, 192, 227, 267, 316, 372, 440, 518, 612, 722, 852, 1006, 1187, 1401, 1654, 1952, 2304, 2720, 3210, 3790, 4473, 5281, 6233, 7358, 8685, 10253, 12102

Offset: 0

Bruno Berselli, Apr 21 2012

nonn

a(n)/a(n-1) tends to (1+sqrt(37))/6 = 1.180460421716369948...

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

Cf. A064650, A182229, A182280; A188935.

a182281 n = a182281_list !! n
a182281_list = 2 : 3 : zipWith (+)
                       a182281_list (map (flip div 3) $ tail a182281_list)
-- Reinhard Zumkeller, Apr 30 2015

[n le 2 select n+1 else Floor(Self(n-1)/3)+Self(n-2): n in [1..55]];

RecurrenceTable[{a[0] == 2, a[1] == 3, a[n] == Floor[a[n - 1]/3] + a[n - 2]}, a, {n, 54}]
Transpose[NestList[{#[[2]],Floor[#[[2]]/3]+#[[1]]}&,{2,3},60]][[1]] (* Harvey P. Dale, Nov 26 2015 *)

cp's OEIS Frontend

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

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

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A182281 a(n) = floor(a(n-1)/3)+a(n-2) with a(0)=2, a(1)=3.

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Haskell

Magma

Mathematica