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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 17 23:07 EDT 2022. Contains 353779 sequences. (Running on oeis4.)