A195223 Number of lower triangles of a 5 X 5 integer array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by n or less and triangles differing by a constant counted only once.

111031, 92031109, 9032683465, 289301569283, 4677360495205, 47764170577925, 350767341744137, 2010235691940497, 9496465116615081, 38429133040711965, 136997589911672127, 439401533118090493, 1288688520518224397

Offset: 1

Author

R. H. Hardin, Sep 13 2011

Keywords

• nonn

Comments

Row 5 of A195220.

Examples

			Some solutions for n=5:
  0               0               0               0               0
  2  4            5  2            3  3            1  5            1  4
  7  2  3         1  5  6         5  7  6         2  3  2        -1  0 -1
  5  4  3  7      2  4  1  1      3  8  7  3      5  6  3  0      0  3  0  2
  6  5  6  2  5   5  3  6  3  1   5  3  5  6  2   9  7  2  0  0   5  3 -1  4  3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..43

Crossrefs

Cf. A195220.

Formula

Empirical: a(n) = (3508493543/18345600)*n^14 + (3508493543/2620800)*n^13 + (1116775769537/239500800)*n^12 + (422094048023/39916800)*n^11 + (377328209183/21772800)*n^10 + (78475421219/3628800)*n^9 + (1073748492569/50803200)*n^8 + (19848770813/1209600)*n^7 + (221251862417/21772800)*n^6 + (18121075223/3628800)*n^5 + (10435002133/5443200)*n^4 + (505904317/907200)*n^3 + (8793472607/75675600)*n^2 + (1397863/90090)*n + 1.

Since a(n) is an Ehrhart polynomial of degree 14 (see A195220), and the empirical polynomial fits the Data for 1 <= n <= 15, it must be correct. - Robert Israel, Oct 06 2019