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A195237
Number of lower triangles of a 7 X 7 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.
1
268435456, 1663418313, 3601738548, 5618308863, 7640055854, 9661943973, 11683832092, 13705720211, 15727608330, 17749496449, 19771384568, 21793272687, 23815160806, 25837048925, 27858937044, 29880825163, 31902713282, 33924601401
OFFSET
1,1
COMMENTS
Row 7 of A195232.
LINKS
FORMULA
Empirical: a(n) = 2021888119*n - 2469384741 for n>4.
Conjectures from Colin Barker, May 06 2018: (Start)
G.f.: x*(268435456 + 1126547401*x + 543337378*x^2 + 78250080*x^3 + 5176676*x^4 + 141128*x^5) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>6.
(End)
EXAMPLE
Some solutions for n=6 with 0 and 6:
..6..............0..............0..............0..............6
..5.5............1.1............1.1............1.1............5.5
..4.4.4..........2.2.2..........1.2.2..........2.2.2..........4.4.4
..4.3.3.3........3.3.3.3........1.1.2.3........2.3.3.3........3.3.3.3
..4.3.2.2.2......3.4.3.4.4......0.1.2.3.4......3.2.3.3.4......2.2.2.2.2
..3.3.3.2.2.1....3.4.4.4.5.5....1.1.2.3.4.5....2.3.2.3.4.5....1.2.2.2.1.1
..4.3.3.2.1.1.0..4.4.4.5.4.5.6..2.1.2.3.4.5.6..3.2.2.3.4.5.6..2.2.2.2.2.1.0
CROSSREFS
Cf. A195232.
Sequence in context: A011578 A223605 A223698 * A194936 A195253 A122969
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 13 2011
STATUS
approved