A318068 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A318068

T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 5, 1, 2, 18, 18, 2, 3, 67, 98, 67, 3, 5, 249, 649, 649, 249, 5, 8, 925, 4003, 7170, 4003, 925, 8, 13, 3437, 25106, 76927, 76927, 25106, 3437, 13, 21, 12770, 156846, 829137, 1405892, 829137, 156846, 12770, 21, 34, 47447, 980960, 8929364, 25994502

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

Table starts

..0.....1.......1..........2............3..............5................8

..1.....5......18.........67..........249............925.............3437

..1....18......98........649.........4003..........25106...........156846

..2....67.....649.......7170........76927.........829137..........8929364

..3...249....4003......76927......1405892.......25994502........479322719

..5...925...25106.....829137.....25994502......824452611......26085599617

..8..3437..156846....8929364....479322719....26085599617....1415459855958

.13.12770..980960...96178466...8844178475...825766558967...76853282341918

.21.47447.6133497.1035919809.163160290206.26137612655323.4172233315256556

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -a(n-4)

k=3: [order 11] for n>12

k=4: [order 39]

EXAMPLE

Some solutions for n=5 k=4

..0..1..1..0. .0..0..1..1. .0..1..0..0. .0..1..1..1. .0..1..1..0

..1..1..1..0. .1..0..0..0. .1..0..0..1. .1..0..0..1. .0..0..0..1

..0..1..0..0. .1..1..0..1. .1..0..0..0. .0..0..1..1. .0..1..1..0

..0..0..0..1. .1..0..0..0. .0..0..1..0. .1..0..0..1. .0..1..0..1

..1..0..1..0. .0..1..1..1. .1..1..1..0. .1..0..1..0. .0..0..0..1

CROSSREFS

Column 1 is A000045(n-1).

Sequence in context: A317823 A318430 A318098 * A165449 A019114 A201526

Adjacent sequences: A318065 A318066 A318067 * A318069 A318070 A318071

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 15 2018

STATUS

approved