A220685 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors

1, 114, 5851, 312603, 15978924, 822649205, 42362190063, 2181341369109, 112319870453715, 5783510938076077, 297801401665428743, 15334225523450669062, 789581475759386788696, 40656693721278204870112

Offset

1,2

Comments

Column 5 of A220688

Links

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

Formula

Empirical: a(n) = 35*a(n-1) +673*a(n-2) +8237*a(n-3) +46927*a(n-4) -112480*a(n-5) -3992526*a(n-6) -35333024*a(n-7) -169366609*a(n-8) -361164394*a(n-9) +47195630*a(n-10) +13502054*a(n-11) +495005695*a(n-12) +6209070799*a(n-13) +5791334536*a(n-14) -11945755468*a(n-15) -10812604841*a(n-16) +3004142790*a(n-17) -8986269878*a(n-18) +26749603735*a(n-19) -17268218707*a(n-20) +10625240169*a(n-21) +1286966410*a(n-22) -5196232889*a(n-23) -236330168*a(n-24) +3747662678*a(n-25) -4565014033*a(n-26) +2769440835*a(n-27) -1086425818*a(n-28) +220144889*a(n-29) -12788683*a(n-30) -5653764*a(n-31) +2046130*a(n-32) -331034*a(n-33) +12027*a(n-34) +3632*a(n-35) +36*a(n-36) for n>37

Example

Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.78.68.48.78...00.67.46.46.48...00.00.00.68.48...00.78.68.47.00
.36.24.28.23.27...38.68.48.68.24...00.78.00.28.28...38.27.23.78.00
.00.00.26.34.00...26.24.26.24.00...36.24.00.26.24...23.00.36.24.00

Crossrefs

Sequence in context: A221293 A306194 A112485 * A199249 A199193 A188694

Adjacent sequences: A220682 A220683 A220684 * A220686 A220687 A220688

Keyword

nonn

Author

R. H. Hardin Dec 17 2012

Status

approved