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 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

%I #4 Dec 17 2012 16:00:42

%S 1,64,968,21380,468036,9973284,215926776,4649097520,100274426148,

%T 2161781726064,46610315291176,1004947894341776,21667343299533216,

%U 467162949559451872,10072346715299691680,217166673508579018784

%N 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

%C Column 5 of A220681

%H R. H. Hardin, <a href="/A220678/b220678.txt">Table of n, a(n) for n = 1..210</a>

%F 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)

%e Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)

%e .00.00.00.68.48...00.67.48.00.78...00.00.00.00.00...00.00.00.67.47

%e .68.48.68.24.27...36.47.27.38.27...00.78.00.00.00...68.47.38.38.00

%e .26.24.26.34.00...36.34.00.23.00...36.24.00.00.00...23.00.26.24.00

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 17 2012

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Last modified August 5 02:37 EDT 2024. Contains 374935 sequences. (Running on oeis4.)