A253748 - OEIS

%I #6 Jan 11 2015 10:22:03

%S 315576,298760,2363797,7348144,33767784,106040628,333213583,871426149,

%T 2111246736,4561812863,9330585017,17842432139,32535281473,56464375423,

%U 94767234632,153713251358,242566893076,372616947142,560429992326

%N Number of (n+1)X(7+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically

%C Column 7 of A253749

%H R. H. Hardin, <a href="/A253748/b253748.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -10*a(n-4) -24*a(n-5) +74*a(n-6) -100*a(n-7) +65*a(n-8) +30*a(n-9) -145*a(n-10) +200*a(n-11) -140*a(n-12) +140*a(n-14) -200*a(n-15) +145*a(n-16) -30*a(n-17) -65*a(n-18) +100*a(n-19) -74*a(n-20) +24*a(n-21) +10*a(n-22) -20*a(n-23) +15*a(n-24) -6*a(n-25) +a(n-26) for n>41

%F Empirical for n mod 4 = 0: a(n) = (31/67200)*n^10 + (7751/60480)*n^9 + (466561/40320)*n^8 + (7477567/20160)*n^7 - (6191923/28800)*n^6 + (19844983/5760)*n^5 - (16432778519/161280)*n^4 + (43453946273/120960)*n^3 + (15278661557/8400)*n^2 - (226744085/28)*n - 1302534 for n>15

%F Empirical for n mod 4 = 1: a(n) = (31/67200)*n^10 + (7751/60480)*n^9 + (466561/40320)*n^8 + (7477567/20160)*n^7 - (6191923/28800)*n^6 + (19844983/5760)*n^5 - (16379257499/161280)*n^4 + (22983106039/60480)*n^3 + (279237392087/134400)*n^2 - (26796876895/2688)*n + (1031330999/512) for n>15

%F Empirical for n mod 4 = 2: a(n) = (31/67200)*n^10 + (7751/60480)*n^9 + (466561/40320)*n^8 + (7477567/20160)*n^7 - (6191923/28800)*n^6 + (19844983/5760)*n^5 - (16443929519/161280)*n^4 + (42972543743/120960)*n^3 + (12531654707/8400)*n^2 - (3312534991/672)*n - (272889211/32) for n>15

%F Empirical for n mod 4 = 3: a(n) = (31/67200)*n^10 + (7751/60480)*n^9 + (466561/40320)*n^8 + (7477567/20160)*n^7 - (6191923/28800)*n^6 + (19844983/5760)*n^5 - (16406990099/161280)*n^4 + (11087479997/30240)*n^3 + (235087208387/134400)*n^2 - (17381962057/2688)*n - (3516359385/512) for n>15

%e Some solutions for n=1

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 11 2015