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A202512 Number of zero-sum -n..n arrays of 4 elements with first through third differences also in -n..n. 1

%I #10 Jun 01 2018 06:02:00

%S 1,15,29,75,115,217,297,479,609,887,1091,1493,1765,2315,2689,3399,

%T 3875,4777,5373,6491,7213,8555,9439,11041,12061,13947,15157,17331,

%U 18719,21221,22809,25663,27453,30659,32699,36301,38545,42567,45089,49527,52303,57205

%N Number of zero-sum -n..n arrays of 4 elements with first through third differences also in -n..n.

%C Row 4 of A202511.

%H R. H. Hardin, <a href="/A202512/b202512.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = -a(n-1) +2*a(n-3) +4*a(n-4) +2*a(n-5) -a(n-6) -5*a(n-7) -5*a(n-8) -a(n-9) +2*a(n-10) +4*a(n-11) +2*a(n-12) -a(n-14) -a(n-15).

%F Empirical g.f.: x*(1 + 16*x + 44*x^2 + 102*x^3 + 156*x^4 + 212*x^5 + 219*x^6 + 208*x^7 + 153*x^8 + 100*x^9 + 46*x^10 + 18*x^11 + 2*x^12 - x^14) / ((1 - x)^4*(1 + x)^3*(1 + x^2)^2*(1 + x + x^2)^2). - _Colin Barker_, Jun 01 2018

%e Some solutions for n=7:

%e .-3....1....2....7....6....5...-2....2....2....2....7...-2...-5...-1....2...-3

%e ..0....2....2....2....1....4...-1...-1....1....3....2....1...-3....2....0....0

%e ..2....2....1...-2...-2...-2....1...-3....0....0...-3....3....1....2....0....3

%e ..1...-5...-5...-7...-5...-7....2....2...-3...-5...-6...-2....7...-3...-2....0

%Y Cf. A202511.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 20 2011

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Last modified February 27 19:24 EST 2024. Contains 370378 sequences. (Running on oeis4.)