cp's OEIS Frontend

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

%I A212532 #8 Jul 20 2018 14:47:52
%S A212532 4,4,7,10,15,15,24,29,39,45,57,65,83,92,111,127,149,163,193,213,245,
%T A212532 270,305,333,378,408,455,496,547,587,650,697,763,819,889,949,1033,
%U A212532 1096,1183,1261,1353,1431,1539,1625,1737,1836,1953,2057,2192,2300,2439,2566,2711
%N A212532 Number of nondecreasing sequences of n 1..4 integers with every element dividing the sequence sum.
%C A212532 Column 4 of A212536.
%H A212532 R. H. Hardin, <a href="/A212532/b212532.txt">Table of n, a(n) for n = 1..210</a>
%F A212532 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).
%F A212532 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
%e A212532 Some solutions for n=8:
%e A212532 ..1....4....2....2....1....1....1....2....1....1....1....2....3....1....1....1
%e A212532 ..1....4....2....3....1....1....1....2....1....2....1....2....3....1....1....3
%e A212532 ..2....4....2....3....1....2....1....4....1....2....3....2....3....1....2....3
%e A212532 ..4....4....2....3....3....2....1....4....1....2....3....2....3....1....2....3
%e A212532 ..4....4....4....3....3....2....1....4....1....2....4....2....3....1....2....3
%e A212532 ..4....4....4....3....3....2....1....4....1....3....4....2....3....1....4....3
%e A212532 ..4....4....4....3....3....2....2....4....2....3....4....4....3....3....4....4
%e A212532 ..4....4....4....4....3....4....2....4....4....3....4....4....3....3....4....4
%Y A212532 Cf. A212536.
%K A212532 nonn
%O A212532 1,1
%A A212532 _R. H. Hardin_, May 20 2012