A232259 - OEIS

%I #6 May 20 2021 13:00:53

%S 37,421,6189,96999,1532151,24091773,379188715,5968365535,93937508717,

%T 1478515964441,23270869263099,366268254468541,5764822631732253,

%U 90734534111164597,1428102170660550681,22477393302841813171

%N Number of (2+1) X (n+1) 0..2 arrays with every element both >= and <= some horizontal or antidiagonal neighbor.

%C Row 2 of A232257.

%H R. H. Hardin, <a href="/A232259/b232259.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-1) -35*a(n-2) +251*a(n-3) -177*a(n-4) -17*a(n-5) -4903*a(n-6) +13125*a(n-7) -76030*a(n-8) +243198*a(n-9) -125167*a(n-10) +449227*a(n-11) -1759711*a(n-12) -678561*a(n-13) -14380759*a(n-14) +17235787*a(n-15) +29891739*a(n-16) +56869843*a(n-17) +17296835*a(n-18) -304146071*a(n-19) -10084543*a(n-20) +293690705*a(n-21) -289132422*a(n-22) +130389906*a(n-23) +513783546*a(n-24) -385905598*a(n-25) -127784349*a(n-26) +309897827*a(n-27) -289851977*a(n-28) -85311709*a(n-29) +219446909*a(n-30) -98649371*a(n-31) -26673126*a(n-32) +86391170*a(n-33) -33068565*a(n-34) -6799239*a(n-35) +22998341*a(n-36) -9045789*a(n-37) -3030746*a(n-38) +2050124*a(n-39) -2846970*a(n-40) -1083162*a(n-41) +282255*a(n-42) -129615*a(n-43) +66349*a(n-44) +183335*a(n-45) +17378*a(n-46) +76502*a(n-47) -4717*a(n-48) +18891*a(n-49) -5877*a(n-50) +2935*a(n-51) -1459*a(n-52) +249*a(n-53) -134*a(n-54) +8*a(n-55) -4*a(n-56) for n > 58.

%e Some solutions for n=4

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

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

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

%Y Cf. A232257.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 21 2013