A220652 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two king-move neighbors, without 3-loops

1, 1, 1, 1, 4, 1, 1, 23, 23, 1, 1, 83, 333, 83, 1, 1, 344, 4352, 4352, 344, 1, 1, 1441, 59846, 192413, 59846, 1441, 1, 1, 5881, 816159, 8627817, 8627817, 816159, 5881, 1, 1, 24220, 11131560, 389859889, 1233993907, 389859889, 11131560, 24220, 1, 1, 99767

Offset

1,5

Comments

Table starts

.1.......1...........1..............1................1.................1

.1.......4..........23.............83..............344..............1441

.1......23.........333...........4352............59846............816159

.1......83........4352.........192413..........8627817.........389859889

.1.....344.......59846........8627817.......1233993907......179768901595

.1....1441......816159......389859889.....179768901595....85240331175084

.1....5881....11131560....17592276986...26120030149221.40274546959211319

.1...24220...151872860...793772500717.3794284713986274

.1...99767..2071881506.35817153012658

.1..410363.28265332768

.1.1688864

.1

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Example

Some solutions for n=3 k=4 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)
.00.00.78.78...69.47.00.78...69.47.68.48...00.78.69.47...68.48.79.00
.69.34.23.27...36.14.37.28...38.16.24.28...39.28.38.17...29.23.79.18
.00.16.34.00...00.36.46.24...26.46.46.24...00.12.23.00...00.13.00.12

Crossrefs

Sequence in context: A015113 A016519 A113716 * A169654 A357744 A088158

Adjacent sequences: A220649 A220650 A220651 * A220653 A220654 A220655

Keyword

nonn,tabl

Author

R. H. Hardin Dec 17 2012

Status

approved