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

1,2

Comments

Column 4 of A212868.

Links

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

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

Example

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

Crossrefs

Cf. A212868.

Sequence in context: A126785 A295586 A283768 * A026317 A361848 A008768

Adjacent sequences: A212861 A212862 A212863 * A212865 A212866 A212867

Keyword

nonn

Author

R. H. Hardin, May 29 2012

Status

approved