A253746 - OEIS

%I #8 Jan 11 2015 11:01:12

%S 28107,70590,583698,2351928,10966149,36766701,112645903,295452432,

%T 734787935,1658583509,3510427759,6967556836,13254580819,24069157677,

%U 42106383208,71123318652,116864959320,186850930571,291778710900

%N Number of (n+1)X(5+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically

%C Column 5 of A253749

%H R. H. Hardin, <a href="/A253746/b253746.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) = (3217/1612800)*n^10 + (33679/138240)*n^9 + (1422807/143360)*n^8 + (18404459/322560)*n^7 - (368077919/460800)*n^6 + (418588771/46080)*n^5 - (917187479/40320)*n^4 - (3006869237/17280)*n^3 + (76331484091/50400)*n^2 - (289830581/70)*n + 3817900 for n>15

%F Empirical for n mod 4 = 1: a(n) = (3217/1612800)*n^10 + (33679/138240)*n^9 + (1422807/143360)*n^8 + (18404459/322560)*n^7 - (368077919/460800)*n^6 + (418588771/46080)*n^5 - (7213283887/322560)*n^4 - (22717166311/138240)*n^3 + (4818663442399/3225600)*n^2 - (55832024207/13440)*n + (16023849991/4096) for n>15

%F Empirical for n mod 4 = 2: a(n) = (3217/1612800)*n^10 + (33679/138240)*n^9 + (1422807/143360)*n^8 + (18404459/322560)*n^7 - (368077919/460800)*n^6 + (418588771/46080)*n^5 - (1802294623/80640)*n^4 - (349731199/2160)*n^3 + (286627480189/201600)*n^2 - (25624890491/6720)*n + (29304949/8) for n>15

%F Empirical for n mod 4 = 3: a(n) = (3217/1612800)*n^10 + (33679/138240)*n^9 + (1422807/143360)*n^8 + (18404459/322560)*n^7 - (368077919/460800)*n^6 + (418588771/46080)*n^5 - (7166029267/322560)*n^4 - (21877961311/138240)*n^3 + (4564135470799/3225600)*n^2 - (8542155047/2240)*n + (15090544151/4096) for n>15

%e Some solutions for n=2

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 11 2015