A084080 Length of lists created by n substitutions k -> Range[k+1,1,-3] starting with {1}, counting down from k+1 to 1 step -3.

1, 1, 1, 2, 3, 4, 9, 15, 22, 52, 91, 140, 340, 612, 969, 2394, 4389, 7084, 17710, 32890, 53820, 135720, 254475, 420732, 1068012, 2017356, 3362260, 8579560, 16301164, 27343888, 70068713

Offset: 0

Author

Wouter Meeussen, May 11 2003

Keywords

• nonn

Comments

Would appear to coincide with row sums of the inverse of the Riordan array (1-x^3,x(1-x^3)). These row sums have g.f. 1/(1-y-y^3+y^4) where y^4-y+x=0. - Paul Barry, May 10 2005

Examples

			{1}, {2}, {3}, {4, 1}, {5, 2, 2}, {6, 3, 3, 3}, {7, 4, 1, 4, 1, 4, 1, 4, 1}
		

Crossrefs

Cf. A124753.

Programs

Mathematica

Length/@Flatten/@NestList[ # /. k_Integer:>Range[k+1, 1, -3]&, {1}, 21]