A232038 - OEIS

A232038

T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal, vertical or antidiagonal neighbor, with top left element zero

3, 11, 11, 37, 76, 37, 129, 521, 521, 129, 450, 3588, 6958, 3588, 450, 1568, 24719, 94102, 94102, 24719, 1568, 5464, 170270, 1272579, 2504637, 1272579, 170270, 5464, 19041, 1172854, 17207275, 66684606, 66684606, 17207275, 1172854, 19041, 66354

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OFFSET

1,1

COMMENTS

Table starts

......3........11...........37.............129.................450

.....11........76..........521............3588...............24719

.....37.......521.........6958...........94102.............1272579

....129......3588........94102.........2504637............66684606

....450.....24719......1272579........66684606..........3495632937

...1568....170270.....17207275......1775039591........183196162778

...5464...1172854....232668433.....47248648693.......9600712297741

..19041...8078859...3146033503...1257683786423.....503143350126954

..66354..55648831..42539187117..33477537844376...26368170190670693

.231230.383320506.575194892084.891118676917809.1381873328000465699

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..312

FORMULA

Empirical for column k:

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

k=2: a(n) = 7*a(n-1) -5*a(n-3) -2*a(n-4) -a(n-5) +2*a(n-6) +2*a(n-7) for n>8

k=3: [order 20]

k=4: [order 42] for n>44

k=5: [order 95] for n>97

EXAMPLE

Some solutions for n=3 k=4

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

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

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

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

CROSSREFS

Sequence in context: A168378 A248410 A059200 * A072980 A128500 A365037

Adjacent sequences: A232035 A232036 A232037 * A232039 A232040 A232041

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 17 2013

STATUS

approved