A265977 - OEIS

%I #5 Dec 19 2015 10:38:01

%S 5,117,1267,13894,262258,3699605,50337359,795864688,11746148349,

%T 169677283808,2554251942699,37889834001861,557236694392506,

%U 8286488663335210,122880923068301625,1816766865705440009

%N Number of nX3 integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors less than itself.

%C Column 3 of A265981.

%H R. H. Hardin, <a href="/A265977/b265977.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +45*a(n-2) +1738*a(n-3) +241*a(n-4) -25197*a(n-5) -495656*a(n-6) -795221*a(n-7) +9824295*a(n-8) +35904715*a(n-9) +85518738*a(n-10) -1045590082*a(n-11) -990640390*a(n-12) +8602945338*a(n-13) -23039489472*a(n-14) +105555033244*a(n-15) +64909267804*a(n-16) -1438654444136*a(n-17) +5711688188760*a(n-18) +1886646031184*a(n-19) +5397581395776*a(n-20) +94830679989552*a(n-21) -249706970454624*a(n-22) -160537012999616*a(n-23) +104471124991808*a(n-24) -2427195586795904*a(n-25) +2670154120634368*a(n-26) +277155463950336*a(n-27) -636551943144960*a(n-28) +2571429999009792*a(n-29) -3778468820090880*a(n-30) +4033571042287616*a(n-31) -2257178070351872*a(n-32) +455329837744128*a(n-33) -33761016152064*a(n-34) +5448728051712*a(n-35) for n>36

%e Some solutions for n=4

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

%e ..0..6..1....0..0..3....2..0..2....0..0..3....2..2..3....0..6..1....3..0..3

%e ..1..1..2....3..1..3....0..0..0....2..0..2....2..0..2....1..1..2....3..0..3

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

%Y Cf. A265981.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2015