A180235 Demi-tribonacci numbers (rounding up): a(0)=a(1)=0, a(2)=2; a(n) = ceiling( (a(n-1)+a(n-2)+a(n-3))/2 ).

0, 0, 2, 1, 2, 3, 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, 37357, 46089, 56863

Offset: 0

Author

Carl R. White, Aug 18 2010

Keywords

• easy
• nonn

Crossrefs

Cf. A000213, A180234

Programs

Mathematica

RecurrenceTable[{a[0]==a[1]==0,a[2]==2,a[n]==Ceiling[(a[n-1]+a[n-2]+ a[n-3])/2]},a,{n,60}] (* Harvey P. Dale, Dec 03 2011 *)

Formula

a(0)=a(1)=0, a(2)=2; a(n) = ceiling( (a(n-1)+a(n-2)+a(n-3))/2 )

For n>5, a(n)=A180234(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