A220637 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal or antidiagonal neighbors

1, 1, 21, 1081, 49448, 1932695, 72097810, 2685329069, 100377946990, 3759405889469, 140807441642550, 5273589943694582, 197503772671988555, 7396752550237211667, 277016765034509275485, 10374589395033217351070

Offset

1,3

Comments

Row 7 of A220632

Links

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

Formula

Empirical: a(n) = 64*a(n-1) -919*a(n-2) -8570*a(n-3) +216353*a(n-4) +531044*a(n-5) -21261655*a(n-6) -32609802*a(n-7) +1171199810*a(n-8) +2109648488*a(n-9) -39063293438*a(n-10) -92688824988*a(n-11) +805714999129*a(n-12) +2451647584900*a(n-13) -10235971284893*a(n-14) -39686089670614*a(n-15) +77545474788177*a(n-16) +406392430654220*a(n-17) -310370552865987*a(n-18) -2718695732195110*a(n-19) +210699841602232*a(n-20) +12228246476518236*a(n-21) +4161966890556370*a(n-22) -37977869919855064*a(n-23) -22915950784622786*a(n-24) +83551109201976972*a(n-25) +64155355218097920*a(n-26) -133459785405218204*a(n-27) -114791737399493541*a(n-28) +158383696504733072*a(n-29) +141093830957446007*a(n-30) -142389992780977126*a(n-31) -123172425999322826*a(n-32) +98262359403451972*a(n-33) +77694058934774432*a(n-34) -52288937671239360*a(n-35) -35710455324063520*a(n-36) +21366553927398268*a(n-37) +11998414558707900*a(n-38) -6636734211915116*a(n-39) -2945615880166783*a(n-40) +1547201872012720*a(n-41) +525999708944081*a(n-42) -266869650005278*a(n-43) -67611096067185*a(n-44) +33461039766336*a(n-45) +6135683963135*a(n-46) -2975024785990*a(n-47) -380281115163*a(n-48) +180562165772*a(n-49) +15221629883*a(n-50) -7030915042*a(n-51) -357383528*a(n-52) +157690672*a(n-53) +4153756*a(n-54) -1668248*a(n-55) -18816*a(n-56) +6272*a(n-57) for n>63

Example

Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.00.00...00.00.00...00.67.47...00.00.00...00.67.47...00.00.00...00.00.00
.00.00.00...00.67.47...36.34.00...00.00.00...36.34.00...00.67.47...00.00.00
.00.00.00...36.34.00...00.00.00...00.67.47...00.67.47...36.34.00...00.00.00
.00.00.00...00.00.00...00.67.47...36.34.00...36.34.00...00.00.00...00.00.00
.00.67.47...00.00.00...36.34.00...00.67.47...00.67.47...00.00.00...00.00.00
.36.34.00...00.67.47...00.67.47...36.34.00...36.34.00...00.00.00...00.67.47
.00.00.00...36.34.00...36.34.00...00.00.00...00.00.00...00.00.00...36.34.00

Crossrefs

Sequence in context: A218821 A012153 A231521 * A143003 A193156 A012183

Adjacent sequences: A220634 A220635 A220636 * A220638 A220639 A220640

Keyword

nonn

Author

R. H. Hardin Dec 17 2012

Status

approved