A220678 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without consecutive collinear links

1, 64, 968, 21380, 468036, 9973284, 215926776, 4649097520, 100274426148, 2161781726064, 46610315291176, 1004947894341776, 21667343299533216, 467162949559451872, 10072346715299691680, 217166673508579018784

Offset

1,2

Comments

Column 5 of A220681

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +406*a(n-2) +1208*a(n-3) -36756*a(n-4) -131648*a(n-5) +1782256*a(n-6) +5363688*a(n-7) -58068352*a(n-8) -116390144*a(n-9) +1320791360*a(n-10) +1428668032*a(n-11) -20544374176*a(n-12) -10237933920*a(n-13) +212753800320*a(n-14) +80515472704*a(n-15) -1459409133184*a(n-16) -1336475701376*a(n-17) +7004200527232*a(n-18) +16996133721728*a(n-19) -26173120065792*a(n-20) -133113887123712*a(n-21) +77894420516608*a(n-22) +711837095810048*a(n-23) -149133534374656*a(n-24) -2573418221750784*a(n-25) -1287866526361088*a(n-26) +8347683197928448*a(n-27) +13083331244459008*a(n-28) -36635386804250624*a(n-29) -24627856431310848*a(n-30) +62991287029956608*a(n-31) +91983827770224640*a(n-32) -113193182713425920*a(n-33) -229939131342147584*a(n-34) +205983685890506752*a(n-35) +340433002255982592*a(n-36) -249334245043159040*a(n-37) -447816498527567872*a(n-38) +525519563320852480*a(n-39) +581499226369556480*a(n-40) -1889006382826520576*a(n-41) -711414396036644864*a(n-42) +4647733236897218560*a(n-43) +2035074403336323072*a(n-44) -8050841158394052608*a(n-45) -6140225542112149504*a(n-46) +10465672271475245056*a(n-47) +11267244041587916800*a(n-48) -8982974963692077056*a(n-49) -14177675512474763264*a(n-50) +3537664858011992064*a(n-51) +12378313020632203264*a(n-52) +1527370012833087488*a(n-53) -6281046064371859456*a(n-54) -2770463486021468160*a(n-55) +464021700166549504*a(n-56) +1019803530220797952*a(n-57) +1830026453979234304*a(n-58) +1156925907500269568*a(n-59) -1016606166756622336*a(n-60) -1593457496406622208*a(n-61) -309420324061970432*a(n-62) +638277543559954432*a(n-63) +431302432367050752*a(n-64) -169489677559005184*a(n-65) -292567436408913920*a(n-66) +884147472039936*a(n-67) +152698367489605632*a(n-68) +69725171782516736*a(n-69) -11451355621228544*a(n-70) -18353073860640768*a(n-71) -8499787523424256*a(n-72) -1186600679636992*a(n-73) +2871864242208768*a(n-74) +1038583221714944*a(n-75) -930083757883392*a(n-76) -513128332787712*a(n-77) +38963943309312*a(n-78) +61710090108928*a(n-79) +9208409882624*a(n-80)

Example

Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.00.00.68.48...00.67.48.00.78...00.00.00.00.00...00.00.00.67.47
.68.48.68.24.27...36.47.27.38.27...00.78.00.00.00...68.47.38.38.00
.26.24.26.34.00...36.34.00.23.00...36.24.00.00.00...23.00.26.24.00

Crossrefs

Sequence in context: A302819 A303512 A000818 * A224162 A224413 A016959

Adjacent sequences: A220675 A220676 A220677 * A220679 A220680 A220681

Keyword

nonn

Author

R. H. Hardin Dec 17 2012

Status

approved