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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..194
Crossrefs
Cf. A195220.
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
Comments