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

1,1

Comments

Row 3 of A202076.

Links

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

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)

Example

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

Crossrefs

Cf. A202076.

Sequence in context: A229573 A337396 A067204 * A280212 A120551 A120547

Adjacent sequences: A202074 A202075 A202076 * A202078 A202079 A202080

Keyword

nonn

Author

R. H. Hardin, Dec 10 2011

Status

approved