A212532 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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.