A220649 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two king-move neighbors, without 3-loops

1, 83, 4352, 192413, 8627817, 389859889, 17592276986, 793772500717, 35817153012658, 1616165851457221, 72925605710399644, 3290593556235156374, 148480170532278144926, 6699812803461818847944, 302313038949065106248425

Offset

1,2

Comments

Column 4 of A220652

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 36*a(n-1) +343*a(n-2) +2931*a(n-3) +9395*a(n-4) -79033*a(n-5) -304578*a(n-6) -236489*a(n-7) +2218923*a(n-8) +4968041*a(n-9) +5876393*a(n-10) +2942035*a(n-11) -19113725*a(n-12) -49387151*a(n-13) +6556425*a(n-14) +14194635*a(n-15) +42787183*a(n-16) -6329582*a(n-17) -8472580*a(n-18) -4501368*a(n-19) +750960*a(n-20) +970734*a(n-21) -47316*a(n-22) -42256*a(n-23) +786*a(n-24) +848*a(n-25)

Example

Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)
.68.49.00.78...89.69.49.00...68.46.46.48...00.69.47.00...89.69.46.48
.29.00.13.27...28.18.18.17...26.49.00.27...89.37.19.00...29.18.19.27
.00.16.34.00...26.24.23.00...00.00.13.00...23.16.46.14...00.12.36.14

Crossrefs

Sequence in context: A084299 A017799 A017746 * A252812 A202657 A180846

Adjacent sequences: A220646 A220647 A220648 * A220650 A220651 A220652

Keyword

nonn

Author

R. H. Hardin Dec 17 2012

Status

approved