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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 13:00 EDT 2020. Contains 334657 sequences. (Running on oeis4.)