A201875 - OEIS

%I #8 Feb 15 2018 09:29:55

%S 3,19,45,95,173,285,431,633,879,1183,1557,1999,2509,3117,3803,4581,

%T 5471,6463,7557,8791,10137,11609,13235,14997,16895,18975,21201,23587,

%U 26169,28921,31843,34989,38315,41835,45593,49555,53721,58153,62799,67673,72827

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

%C Row 4 of A201873.

%H R. H. Hardin, <a href="/A201875/b201875.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: (3 + 16*x + 23*x^2 + 28*x^3 + 20*x^4 + 16*x^5 + 3*x^6 + 2*x^7 - x^8) / ((1 - x)^4*(1 + x)*(1 + x + x^2)^2). - _Colin Barker_, Feb 15 2018

%e Some solutions for n=11:

%e ..0...-1....4...-7...-7...10...-1...-6...-9..-11....1....9....4...-8...-4....7

%e ..0....5...-2...-4...-2...-1....1...-3....1...-3...-1....6...-4...-4....4....2

%e ..2....0....1....5...-1...-3...-2....4....5....3....1...-4...-1....2....3...-6

%e .-2...-4...-3....6...10...-6....2....5....3...11...-1..-11....1...10...-3...-3

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 06 2011