A165381 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, 4 in the lower right corner, and with no element having more than 3 neighbors with the same value.

37, 285, 1012, 2467, 4708, 7748, 11588, 16228, 21668, 27908, 34948, 42788, 51428, 60868, 71108, 82148, 93988, 106628, 120068, 134308, 149348, 165188, 181828, 199268, 217508, 236548, 256388, 277028, 298468, 320708, 343748, 367588, 392228

Offset

2,1

Comments

Same recurrence for A165392.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>=9.

Conjectures from Colin Barker, Feb 26 2018: (Start)

G.f.: x^2*(37 + 174*x + 268*x^2 + 249*x^3 + 58*x^4 + 13*x^5 + x^6) / (1 - x)^3.

a(n) = 4*(817 - 540*n + 100*n^2) for n>5.

(End)

Example

Some solutions for n=3:
...1.3.2.2.......1.1.3.2.......1.1.1.2.......1.1.2.2.......1.1.2.2....
.....3.3.2.2.......3.3.2.2.......1.4.4.4.......1.2.2.2.......1.3.2.2..
.......3.3.3.4.......3.3.3.4.......3.4.4.4.......3.3.3.4.......3.2.2.4
------
...1.1.2.2.......1.1.2.2.......1.1.1.2.......1.1.2.2.......1.1.1.2....
.....1.1.1.4.......2.2.2.4.......2.2.2.4.......2.2.4.4.......1.1.2.4..
.......3.1.4.4.......3.4.4.4.......3.4.4.4.......3.4.4.4.......3.3.4.4

Crossrefs

Cf. A165392.

Sequence in context: A142835 A142234 A215632 * A086840 A190418 A200889

Adjacent sequences: A165378 A165379 A165380 * A165382 A165383 A165384

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved