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

19, 127, 475, 1279, 2833, 5509, 9739, 16039, 25003, 37279, 53605, 74797, 101719, 135331, 176671, 226819, 286957, 358345, 442279, 540163, 653479, 783739, 932569, 1101673, 1292779, 1507735, 1748467, 2016919, 2315161, 2645341, 3009619, 3410287

Offset: 1

Author

R. H. Hardin, Dec 11 2011

Keywords

• nonn

Comments

Row 4 of A202124.

Examples

			Some solutions for n=5:
  -4   1   0   1  -2   2   3  -3  -2   2   2   1   3  -1  -1   2
  -4  -4  -4  -1  -2   0   2   0  -4   2   2  -1  -1   0  -1   4
  -1  -5  -4  -2   0  -1   0   4  -2   2   0   0  -3  -2  -1   4
   1  -5   1   1   1   0   0   5   1   4  -4   1   0  -5   4   1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Cf. A202124.

Formula

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).

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