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

1, 2356, 172833, 49406943, 8011414792, 1637496710797, 304265433695569, 58792186589810692, 11178980566694533181, 2139705888320467053783, 408438850253554118760672, 78052060676212571885932839

Offset

1,2

Comments

Row 7 of A220621

Links

R. H. Hardin, Table of n, a(n) for n = 1..165

Formula

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)

Example

Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10)
..0..7..0....0..9..0....0..7..0....0..7..0....0..0..0....0..6..4....0..6..4
..3..9..0....0..7..1....3..7..0....3..7..0....0..7..0....6..4..0....6..4..0
..0..9..1....3..0..0....3..6..4....3..7..0....3..7..0....9..7..0....0..7..0
..0..7..1....0..6..4....0..9..0....3..7..0....3..6..4....3..1..0....3..0..0
..3..7..7....0..7..0....6..4..1....3..0..7....6..4..0....0..6..4....0..6..4
..3..3..0....3..9..0....0..7..0....0..3..0....0..7..7....0..9..0....0..9..7
..6..4..0....6..4..1....3..0..0....0..0..0....3..3..0....0..0..1....0..3..1

Crossrefs

Sequence in context: A035874 A226267 A251295 * A136420 A132391 A346940

Adjacent sequences: A220623 A220624 A220625 * A220627 A220628 A220629

Keyword

nonn

Author

R. H. Hardin Dec 17 2012

Status

approved