A212532 Number of nondecreasing sequences of n 1..4 integers with every element dividing the sequence sum.

4, 4, 7, 10, 15, 15, 24, 29, 39, 45, 57, 65, 83, 92, 111, 127, 149, 163, 193, 213, 245, 270, 305, 333, 378, 408, 455, 496, 547, 587, 650, 697, 763, 819, 889, 949, 1033, 1096, 1183, 1261, 1353, 1431, 1539, 1625, 1737, 1836, 1953, 2057, 2192, 2300, 2439, 2566, 2711

Offset: 1

Author

R. H. Hardin, May 20 2012

Keywords

• nonn

Comments

Column 4 of A212536.

Examples

			Some solutions for n=8:
..1....4....2....2....1....1....1....2....1....1....1....2....3....1....1....1
..1....4....2....3....1....1....1....2....1....2....1....2....3....1....1....3
..2....4....2....3....1....2....1....4....1....2....3....2....3....1....2....3
..4....4....2....3....3....2....1....4....1....2....3....2....3....1....2....3
..4....4....4....3....3....2....1....4....1....2....4....2....3....1....2....3
..4....4....4....3....3....2....1....4....1....3....4....2....3....1....4....3
..4....4....4....3....3....2....2....4....2....3....4....4....3....3....4....4
..4....4....4....4....3....4....2....4....4....3....4....4....3....3....4....4
		

Links

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

Crossrefs

Cf. A212536.

Formula

Empirical: a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6) + a(n-12) - a(n-13) - a(n-14) + a(n-16) + a(n-17) - a(n-18).

Empirical g.f.: x*(4 - x^2 - x^3 + 2*x^4 - 2*x^5 + x^6 + 3*x^7 + 4*x^8 - 3*x^9 - 3*x^10 + x^11 + x^12 - x^13 + 2*x^15 - x^17) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2*(1 - x^2 + x^4)). - Colin Barker, Jul 20 2018