A128094 Number of sequences s of length n, with s[1]=1, s[2]=1, s[3]=1, s[k-1] <=s[k] <= s[k-1]+s[k-2]+s[k-3] (s is called a sub-tribonacci sequence of length n).

1, 3, 9, 36, 228, 2196, 33901, 862503, 36346723, 2564238411, 304902857694, 61384367733677, 21020435566780278, 12292402317454051941, 12319906894146608845054, 21234027294331775378957366

Offset: 3

Author

Emeric Deutsch, Feb 14 2007

Keywords

• nonn

Examples

			a(5)=9 because we have (1,1,1,1,1), (1,1,1,1,2), (1,1,1,1,3), (1,1,1,2,2), (1,1,1,2,3), (1,1,1,2,4), (1,1,1,3,3), (1,1,1,3,4), (1,1,1,3,5).
		

Links

• Peter C. Fishburn and Fred S. Roberts, Elementary sequences, sub-Fibonacci sequences, Discrete Appl. Math. 44 (1993), no. 1-3, 261-281.

Crossrefs

Cf. A005269.

Programs

Maple

f[0]:=1:for k from 0 to 20 do f[k+1]:=factor(sum(subs({x=y, y=z, z=u}, f[k]), u=z..x+y+z)) od: seq(subs({x=1, y=1,z=1}, f[k]), k=0..20);

Formula

See the Maple program; f[k](x,y,z) is the number of sequences s[1], s[2], ..., s[k+3] such that s[1]=x, s[2]=y, s[3]=z, s[j-1] <=s[j] <= s[j-3]+s[j-2]+s[j-1].