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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. 1
111031, 92031109, 9032683465, 289301569283, 4677360495205, 47764170577925, 350767341744137, 2010235691940497, 9496465116615081, 38429133040711965, 136997589911672127, 439401533118090493, 1288688520518224397 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 5 of A195220.

LINKS

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

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

EXAMPLE

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

CROSSREFS

Cf. A195220.

Sequence in context: A146888 A175535 A103874 * A205243 A223110 A094325

Adjacent sequences: A195220 A195221 A195222 * A195224 A195225 A195226

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 13 2011

STATUS

approved

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Last modified January 27 17:42 EST 2023. Contains 359845 sequences. (Running on oeis4.)