A195222 Number of lower triangles of a 4 X 4 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.

2277, 176471, 3395245, 31640829, 189677411, 845613769, 3048698613, 9369900047, 25430520379, 62478288201, 141479051231, 299315365855, 597820942629, 1136532061199, 2070203713171, 3632319367413, 6166018879097, 10164079181491

Offset

1,1

Comments

Row 4 of A195220.

Links

R. H. Hardin, Table of n, a(n) for n = 1..194

Formula

Empirical: a(n) = (1207573/30240)*n^9 + (1207573/6720)*n^8 + (1000157/2520)*n^7 + (264247/480)*n^6 + (754417/1440)*n^5 + (338651/960)*n^4 + (2533393/15120)*n^3 + (90763/1680)*n^2 + (901/84)*n + 1.

Since a(n) is an Ehrhart polynomial of degree 9 (see A195220), and the empirical polynomial fits the Data for 1 <= n <= 10, it must be correct. - Robert Israel, Oct 06 2019

Example

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

Crossrefs

Cf. A195220.

Sequence in context: A260206 A349941 A349938 * A205165 A166222 A203725

Adjacent sequences: A195219 A195220 A195221 * A195223 A195224 A195225

Keyword

nonn

Author

R. H. Hardin, Sep 13 2011

Status

approved