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A202125 Number of -n..n arrays of 4 elements with first, second and third differences also in -n..n. 2

%I

%S 19,127,475,1279,2833,5509,9739,16039,25003,37279,53605,74797,101719,

%T 135331,176671,226819,286957,358345,442279,540163,653479,783739,

%U 932569,1101673,1292779,1507735,1748467,2016919,2315161,2645341,3009619,3410287

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

%C Row 4 of A202124.

%H R. H. Hardin, <a href="/A202125/b202125.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(19 + 70*x + 151*x^2 + 178*x^3 + 154*x^4 + 70*x^5 + 19*x^6 - 2*x^7 + x^8) / ((1 - x)^5*(1 + x + x^2)^2). - _Colin Barker_, Mar 03 2018

%e Some solutions for n=5:

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

%e -4 -4 -4 -1 -2 0 2 0 -4 2 2 -1 -1 0 -1 4

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

%e 1 -5 1 1 1 0 0 5 1 4 -4 1 0 -5 4 1

%Y Cf. A202124.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 11 2011

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Last modified June 26 10:23 EDT 2022. Contains 354879 sequences. (Running on oeis4.)