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

1,1

Comments

Column 4 of A212536.

Links

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

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

Example

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

Crossrefs

Cf. A212536.

Sequence in context: A185670 A011981 A238131 * A109544 A187893 A293678

Adjacent sequences: A212529 A212530 A212531 * A212533 A212534 A212535

Keyword

nonn

Author

R. H. Hardin, May 20 2012

Status

approved