A165373 Number of slanted n X 4 (i=1..n) X (j=i..4+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, and 4 in the lower right corner.

37, 305, 1409, 4569, 11449, 24225, 45585, 78729, 127369, 195729, 288545, 411065, 569049, 768769, 1017009, 1321065, 1688745, 2128369, 2648769, 3259289, 3969785, 4790625, 5732689, 6807369, 8026569, 9402705, 10948705, 12678009, 14604569

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n=2..99

Formula

Empirical: a(n) = 5*a(n-1) - 10*a(n-2) +10*a(n-3) - 5*a(n-4) + a(n-5) for n>=8.

Conjectures from Colin Barker, Mar 25 2018: (Start)

G.f.: x^2*(37 + 120*x + 254*x^2 + 204*x^3 - 171*x^4 + 68*x^5) / (1 - x)^5.

a(n) = (1107 - 1060*n + 716*n^2 - 320*n^3 + 64*n^4) / 3 for n>2.

(End)

Example

Some solutions for n=3:
...1.2.2.2.......1.1.2.2.......1.1.2.2.......1.1.2.2.......1.1.1.2....
.....2.3.2.2.......1.1.1.1.......4.4.4.4.......1.1.2.2.......2.2.2.4..
.......3.3.3.4.......3.1.1.4.......3.3.4.4.......3.3.3.4.......3.2.4.4
------
...1.1.2.2.......1.1.2.2.......1.1.1.2.......1.1.1.2.......1.1.1.2....
.....1.1.3.3.......1.2.2.2.......1.2.2.2.......4.4.4.4.......3.3.2.4..
.......3.3.4.4.......3.2.2.4.......3.2.4.4.......3.3.4.4.......3.2.4.4

Crossrefs

Sequence in context: A211156 A217642 A197340 * A165292 A114785 A061014

Adjacent sequences: A165370 A165371 A165372 * A165374 A165375 A165376

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved