A212864 Number of nondecreasing sequences of n 1..4 integers with no element dividing the sequence sum.

0, 2, 3, 5, 6, 9, 12, 15, 17, 22, 26, 30, 34, 40, 45, 51, 56, 63, 70, 77, 83, 92, 100, 108, 116, 126, 135, 145, 154, 165, 176, 187, 197, 210, 222, 234, 246, 260, 273, 287, 300, 315, 330, 345, 359, 376, 392, 408, 424, 442, 459, 477, 494, 513, 532, 551, 569, 590, 610, 630, 650

Offset: 1

Author

R. H. Hardin, May 29 2012

Keywords

• nonn

Comments

Column 4 of A212868.

Examples

			All solutions for n=8:
..2....2....2....2....2....2....3....2....2....3....2....2....2....3....3
..2....3....2....2....2....2....3....2....3....3....2....3....2....4....3
..3....3....2....2....2....2....3....3....4....3....2....3....2....4....3
..3....3....2....2....2....2....3....3....4....3....3....3....3....4....4
..3....3....3....2....2....2....3....3....4....3....4....3....3....4....4
..3....3....4....2....2....3....3....4....4....3....4....3....3....4....4
..3....3....4....3....2....3....4....4....4....3....4....4....4....4....4
..4....3....4....4....3....3....4....4....4....4....4....4....4....4....4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A212868.

Formula

Empirical: a(n) = a(n-1) + a(n-3) - a(n-5) - a(n-7) + a(n-8).

Empirical g.f.: x^2*(2 + x + 2*x^2 - x^3) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jul 21 2018