A239552 Number of compositions of n such that the first part is 1 and the second differences of the parts are in {-2,...,2}.

1, 1, 1, 2, 4, 7, 11, 18, 32, 53, 89, 152, 255, 431, 733, 1243, 2111, 3583, 6087, 10342, 17564, 29845, 50704, 86150, 146382, 248716, 422618, 718091, 1220156, 2073272, 3522846, 5985967, 10171232, 17282786, 29366645, 49899299, 84788109, 144070585, 244802450

Offset: 0

Author

Alois P. Heinz, Mar 21 2014

Keywords

• nonn

Examples

			a(5) = 7: [1,1,1,1,1], [1,1,1,2], [1,1,2,1], [1,1,3], [1,2,1,1], [1,2,2], [1,4].
a(6) = 11: [1,1,1,1,1,1], [1,1,1,1,2], [1,1,1,2,1], [1,1,1,3], [1,1,2,1,1], [1,1,2,2], [1,2,1,1,1], [1,2,1,2], [1,2,2,1], [1,2,3], [1,5].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=2 of A239550.

Formula

a(n) ~ c * d^n, where d = 1.6991842071646453928920987915033839182675484195426953647249305754952..., c = 0.4361924842463814839782496098129122542027259655263562779280217228428... . - Vaclav Kotesovec, Aug 28 2014