A194998 -id:A194998 - cp's OEIS frontend

A195002 Number of lower triangles of a 6 X 6 0..n array with each element differing from all of its horizontal and vertical neighbors by one.

2, 4608, 31042, 81014, 138956, 199988, 261324, 322806, 384292, 445780, 507268, 568756, 630244, 691732, 753220, 814708, 876196, 937684, 999172, 1060660, 1122148, 1183636, 1245124, 1306612, 1368100, 1429588, 1491076, 1552564, 1614052, 1675540

Offset: 1

R. H. Hardin, Sep 07 2011

nonn

Row 6 of A194998.

			Some solutions for n=4:
..4............2............2............4............2............0
..3.4..........3.2..........1.0..........3.4..........3.4..........1.2
..2.3.2........4.3.2........0.1.0........2.3.4........4.3.2........2.3.4
..1.2.3.2......3.2.3.4......1.2.1.2......3.4.3.4......3.4.3.2......1.2.3.2
..0.1.2.3.2....2.3.4.3.2....0.1.0.1.2....2.3.2.3.2....2.3.2.1.2....2.1.2.1.2
..1.2.1.2.1.0..3.4.3.4.3.2..1.2.1.2.1.2..3.2.3.2.3.2..3.2.3.2.1.0..3.2.3.2.1.2

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A194998.

Empirical: a(n) = 61488*n - 169100 for n>8.

Empirical g.f.: 2*x*(1 + 2302*x + 10914*x^2 + 11769*x^3 + 3985*x^4 + 1545*x^5 + 152*x^6 + 73*x^7 + 2*x^8 + x^9) / (1 - x)^2. - Colin Barker, May 06 2018

A195003 Number of lower triangles of a 7 X 7 0..n array with each element differing from all of its horizontal and vertical neighbors by one.

Original entry on oeis.org

2, 69632, 641376, 2059822, 3816148, 5740166, 7686580, 9643120, 11600228, 13557614, 15515004, 17472396, 19429788, 21387180, 23344572, 25301964, 27259356, 29216748, 31174140, 33131532, 35088924, 37046316, 39003708, 40961100, 42918492

Offset: 1

R. H. Hardin, Sep 07 2011

nonn

Row 7 of A194998.

			Some solutions for n=4:
..0..............0..............0..............0..............0
..1.0............1.0............1.0............1.0............1.0
..2.1.2..........0.1.2..........0.1.2..........2.1.2..........2.1.2
..1.2.1.2........1.0.1.2........1.2.1.2........1.2.3.4........1.0.1.2
..2.3.2.1.2......0.1.0.1.2......2.3.2.1.2......2.3.4.3.2......2.1.2.1.2
..1.2.1.2.1.2....1.0.1.0.1.2....1.2.3.2.1.0....1.2.3.2.1.0....1.2.1.0.1.2
..0.1.2.3.2.1.0..2.1.2.1.2.3.2..2.3.2.1.2.1.0..2.3.2.1.0.1.0..2.3.2.1.2.3.2

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A194998.

Empirical: a(n) = 1957392*n - 6016308 for n>10.

Empirical g.f.: 2*x*(1 + 34814*x + 251057*x^2 + 423351*x^3 + 168940*x^4 + 83846*x^5 + 11198*x^6 + 5063*x^7 + 284*x^8 + 139*x^9 + 2*x^10 + x^11) / (1 - x)^2. - Colin Barker, May 06 2018

cp's OEIS Frontend

A195002 Number of lower triangles of a 6 X 6 0..n array with each element differing from all of its horizontal and vertical neighbors by one.

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