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A220626 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.

%I A220626 #6 Jul 23 2025 01:19:02
%S A220626 1,2356,172833,49406943,8011414792,1637496710797,304265433695569,
%T A220626 58792186589810692,11178980566694533181,2139705888320467053783,
%U A220626 408438850253554118760672,78052060676212571885932839
%N A220626 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.
%C A220626 Row 7 of A220621
%H A220626 R. H. Hardin, <a href="/A220626/b220626.txt">Table of n, a(n) for n = 1..165</a>
%F A220626 Empirical: a(n) = 138*a(n-1) +14704*a(n-2) -766832*a(n-3) -28294686*a(n-4) +1524422160*a(n-5) +1505265612*a(n-6) -657053175478*a(n-7) +2442897908716*a(n-8) +121219040652652*a(n-9) -477157654573460*a(n-10) -11078652756436422*a(n-11) +25390010604819866*a(n-12) +462672915130668714*a(n-13) +539039443446704064*a(n-14) -2300750637803847292*a(n-15) -106740256054565434670*a(n-16) -525485832852749557732*a(n-17) +4696460371559704057208*a(n-18) +20625415710589823362046*a(n-19) -106635774503822778533068*a(n-20) -359528017386314652554916*a(n-21) +1434757125253268865522192*a(n-22) +3342419613209446332183086*a(n-23) -12412241250913071404180671*a(n-24) -16009499469215852930982996*a(n-25) +76301561379273628920121480*a(n-26) +16714074472917107500322288*a(n-27) -350287053489912157977657276*a(n-28) +246449516277847669520873504*a(n-29) +1085617448661458748927032552*a(n-30) -1465223004596924237606500724*a(n-31) -1803274128034881610349327880*a(n-32) +3516508917367494771271844688*a(n-33) +684156230546695030907577128*a(n-34) -3371221939576667129347102948*a(n-35) +1774979612482525654248800356*a(n-36) -305960447612303854340530276*a(n-37) -1782960715267049838679389320*a(n-38) +2423880586788763938819482584*a(n-39) +346133788947372810781005124*a(n-40) -1729222868084540777448834968*a(n-41) +266878793131853890601352560*a(n-42) +960049718041715410291124004*a(n-43) -832232703419849484865464104*a(n-44) +183729276922163315799804240*a(n-45) +342523577682868354239921104*a(n-46) -399235979100028148521176332*a(n-47) +120009650652405707129304857*a(n-48) +46551250238969402512573930*a(n-49) -38145714869513667277222872*a(n-50) +7918437257271901469718272*a(n-51) -2635055091367948207000262*a(n-52) +3607443742375711101808688*a(n-53) -2000242792241551629394644*a(n-54) +21899529024947808110922*a(n-55) +356306994648073904663420*a(n-56) -93971649444626647347932*a(n-57) -1450295589197392760916*a(n-58) -1024247136206230000278*a(n-59) +1187176424264486875426*a(n-60) -134415977089345498662*a(n-61) +55717506862783032360*a(n-62) -21553683350249918364*a(n-63) +2674908537678317322*a(n-64) -173994425830551588*a(n-65) +60988142986744248*a(n-66) -8768894100846210*a(n-67) -458136027067500*a(n-68) +84709288120500*a(n-69) -1129653540000*a(n-70) +1588978518750*a(n-71) -165767765625*a(n-72)
%e A220626 Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10)
%e A220626 ..0..7..0....0..9..0....0..7..0....0..7..0....0..0..0....0..6..4....0..6..4
%e A220626 ..3..9..0....0..7..1....3..7..0....3..7..0....0..7..0....6..4..0....6..4..0
%e A220626 ..0..9..1....3..0..0....3..6..4....3..7..0....3..7..0....9..7..0....0..7..0
%e A220626 ..0..7..1....0..6..4....0..9..0....3..7..0....3..6..4....3..1..0....3..0..0
%e A220626 ..3..7..7....0..7..0....6..4..1....3..0..7....6..4..0....0..6..4....0..6..4
%e A220626 ..3..3..0....3..9..0....0..7..0....0..3..0....0..7..7....0..9..0....0..9..7
%e A220626 ..6..4..0....6..4..1....3..0..0....0..0..0....3..3..0....0..0..1....0..3..1
%K A220626 nonn
%O A220626 1,2
%A A220626 _R. H. Hardin_ Dec 17 2012