A180235 -id:A180235 - cp's OEIS frontend

A258875 a(1) = a(2) = a(3) = 1; for n > 3, a(n) = ceiling((a(n-1) + a(n-2) + a(n-3))/2).

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 23, 29, 36, 44, 55, 68, 84, 104, 128, 158, 195, 241, 297, 367, 453, 559, 690, 851, 1050, 1296, 1599, 1973, 2434, 3003, 3705, 4571, 5640, 6958, 8585, 10592, 13068, 16123, 19892, 24542, 30279

Offset: 1

Morris Neene, Jun 13 2015

nonn

First 14 terms are the same as A179241.
Ratio of consecutive terms approaches the real root of x^3 - (x^2 + x + 1)/2 = 0, whose approximate value is 1.2337519285, and whose exact value is (1 + (64 - 3*sqrt(417))^(1/3) + (64 + 3*sqrt(417))^(1/3))/6.
Same as A180235 for n > 5. - Georg Fischer, Oct 09 2018

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

[n le 3 select 1 else Ceiling((Self(n-1)+Self(n-2)+ Self(n-3))/2): n in [1..60]]; // Vincenzo Librandi, Oct 10 2018

a(4) = ceiling((1+1+1)/2) = 2;
a(5) = ceiling((1+1+2)/2) = 2;
a(6) = ceiling((1+2+2)/2) = 3.

RecurrenceTable[{a[n] == Ceiling[(a[n - 1] + a[n - 2] + a[n - 3])/2], a[1] == a[2] == a[3] == 1}, a, {n, 1, 49}] (* Michael De Vlieger, Jun 20 2015 *)
nxt[{a_,b_,c_}]:={b,c,Ceiling[(a+b+c)/2]}; NestList[nxt,{1,1,1},50][[All,1]] (* Harvey P. Dale, Feb 03 2022 *)

lista(nn) = {va = vector(nn, n, if (n<=3, 1)); for (n=4, nn, va[n] = ceil((va[n-1]+va[n-2]+va[n-3])/2);); va;} \\ Michel Marcus, Jun 17 2015

A180234 Demi-tribonacci numbers (rounding down): a(0)=a(1)=0, a(2)=2; a(n) = floor( (a(n-1)+a(n-2)+a(n-3))/2 ).

Original entry on oeis.org

0, 0, 2, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 7, 9, 11, 13, 16, 20, 24, 30, 37, 45, 56, 69, 85, 105, 129, 159, 196, 242, 298, 368, 454, 560, 691, 852, 1051, 1297, 1600, 1974, 2435, 3004, 3706, 4572, 5641, 6959, 8586, 10593, 13069, 16124, 19893, 24543, 30280, 37358, 46090

Offset: 0

Carl R. White, Aug 18 2010

Cf. A000213, A180235

a(0)=a(1)=0, a(2)=2; a(n) = floor( (a(n-1)+a(n-2)+a(n-3))/2 )
For n>9, a(n)=A180235(n-4)+1
a(n)/a(n-1) tends to 1.233751928528... which is a root of 2*x^3 - x^2 - x - 1 = 0

cp's OEIS Frontend

A258875 a(1) = a(2) = a(3) = 1; for n > 3, a(n) = ceiling((a(n-1) + a(n-2) + a(n-3))/2).

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A180234 Demi-tribonacci numbers (rounding down): a(0)=a(1)=0, a(2)=2; a(n) = floor( (a(n-1)+a(n-2)+a(n-3))/2 ).

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