A206273 - OEIS

A206273

Number of (n+1) X 5 0..2 arrays with no 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases in its adjacent leftward or upward neighbors.

%I #7 Dec 11 2015 21:24:32

%S 4884,11205,39306,145824,495858,1824315,6254364,22950822,80340090,

%T 297576123,1049291592,3857539692,13593707712,50108727009,177035467728,

%U 652290312486,2303858318196,8487080173464,29999221547154,110520245949639

%N Number of (n+1) X 5 0..2 arrays with no 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases in its adjacent leftward or upward neighbors.

%C Column 4 of A206277.

%H R. H. Hardin, <a href="/A206273/b206273.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 16*a(n-2) +17*a(n-4) -718*a(n-6) -808*a(n-8) +190*a(n-9) +11438*a(n-10) -620*a(n-11) -67647*a(n-12) +3492*a(n-13) +312771*a(n-14) -33638*a(n-15) +1348688*a(n-16) -102062*a(n-17) -853413*a(n-18) -750694*a(n-19) -7005863*a(n-20) -5658450*a(n-21) -25736013*a(n-22) +2139694*a(n-23) +41772730*a(n-24) -53739682*a(n-25) -164352002*a(n-26) +21736512*a(n-27) -2519634*a(n-28) -337012654*a(n-29) -81817424*a(n-30) +250893326*a(n-31) +917258192*a(n-32) -1447771298*a(n-33) -3615704782*a(n-34) -244892440*a(n-35) -7691321895*a(n-36) -2662626796*a(n-37) -12292738880*a(n-38) -2993682446*a(n-39) -10162211538*a(n-40) -7852874164*a(n-41) -31856358785*a(n-42) -200802094*a(n-43) -45550537463*a(n-44) -8070319668*a(n-45) -40592892197*a(n-46) -7781538872*a(n-47) -2259711479*a(n-48) -4398359126*a(n-49) +6341638113*a(n-50) +13027313724*a(n-51) +5351561306*a(n-52) +11253724846*a(n-53) -5223909939*a(n-54) +3668371886*a(n-55) +2746211621*a(n-56) +967459284*a(n-57) +5059156578*a(n-58) +4482864880*a(n-59) +3864467452*a(n-60) +3432722708*a(n-61) +1699749100*a(n-62) +1983595068*a(n-63) +1420608808*a(n-64) +463076952*a(n-65) +968625564*a(n-66) +162765888*a(n-67) +473812528*a(n-68) +71231744*a(n-69) +153455092*a(n-70) +17059712*a(n-71) +38080432*a(n-72) -2547072*a(n-73) +6152688*a(n-74) -676832*a(n-76) for n>82.

%e Some solutions for n=4:

%e ..1..1..2..2..1....2..1..2..0..1....0..2..1..2..2....0..1..2..0..2

%e ..0..2..1..1..2....2..2..0..0..2....0..0..2..2..2....0..1..0..2..2

%e ..1..0..1..1..2....2..2..2..1..0....0..0..2..2..0....0..2..1..2..2

%e ..2..0..0..2..1....1..1..0..2..2....1..1..0..0..1....1..0..1..1..0

%e ..2..2..1..0..1....0..2..1..1..1....1..1..0..0..0....2..0..0..2..1

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 05 2012