A202077 Number of arrays of 5 integers in -n..n with sum zero and the sum of every adjacent pair being odd.

2, 26, 78, 264, 504, 1128, 1786, 3262, 4660, 7540, 10092, 15066, 19278, 27174, 33644, 45428, 54846, 71622, 84770, 107780, 125532, 156156, 179478, 219234, 249184, 299728, 337456, 400582, 447330, 524970, 582072, 676296, 745178, 858194, 940374

Offset: 1

Author

R. H. Hardin, Dec 10 2011

Keywords

• nonn

Comments

Row 3 of A202076.

Examples

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

Links

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

Crossrefs

Cf. A202076.

Formula

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

Conjectures from Colin Barker, May 26 2018: (Start)

G.f.: 2*x*(1 + 12*x + 22*x^2 + 45*x^3 + 22*x^4 + 12*x^5 + x^6) / ((1 - x)^5*(1 + x)^4).

a(n) = (230*n^4 + 552*n^3 + 424*n^2 + 96*n) / 384 for n even.

a(n) = (230*n^4 + 368*n^3 + 148*n^2 + 16*n + 6) / 384 for n odd.

(End)