A253747 Number of (n+1)X(6+1) 0..2 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically

95940, 148134, 1204422, 4249381, 19685575, 64166071, 199063466, 515093745, 1244615026, 2727201405, 5639709716, 10890975382, 20090499351, 35396254577, 60232652786, 98961073673, 158149967837, 246162916176, 374812197446

Offset

1,1

Comments

Column 6 of A253749

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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>40

Empirical for n mod 4 = 0: a(n) = (41/67200)*n^10 + (2027/15120)*n^9 + (6371/672)*n^8 + (19191847/80640)*n^7 - (69687461/57600)*n^6 + (8499037/5760)*n^5 + (842162075/8064)*n^4 - (74838995639/60480)*n^3 + (326248711007/50400)*n^2 - (11101352467/840)*n + 1766327 for n>14

Empirical for n mod 4 = 1: a(n) = (41/67200)*n^10 + (2027/15120)*n^9 + (6371/672)*n^8 + (19191847/80640)*n^7 - (69687461/57600)*n^6 + (8499037/5760)*n^5 + (843084731/8064)*n^4 - (298212052811/241920)*n^3 + (2629235479831/403200)*n^2 - (29593169357/2240)*n + (34190535/32) for n>14

Empirical for n mod 4 = 2: a(n) = (41/67200)*n^10 + (2027/15120)*n^9 + (6371/672)*n^8 + (19191847/80640)*n^7 - (69687461/57600)*n^6 + (8499037/5760)*n^5 + (841274195/8064)*n^4 - (74915448029/60480)*n^3 + (321295813757/50400)*n^2 - (20505342029/1680)*n - (2629905/4) for n>14

Empirical for n mod 4 = 3: a(n) = (41/67200)*n^10 + (2027/15120)*n^9 + (6371/672)*n^8 + (19191847/80640)*n^7 - (69687461/57600)*n^6 + (8499037/5760)*n^5 + (843364451/8064)*n^4 - (296756967011/241920)*n^3 + (2650967418031/403200)*n^2 - (94626072641/6720)*n + (28054555/8) for n>14

Example

Some solutions for n=2
..1..1..0..0..1..1..0....0..0..0..0..0..0..0....0..2..1..0..1..2..2
..1..0..0..1..1..0..0....1..1..0..0..0..0..1....2..1..0..0..1..1..1
..2..0..1..1..0..0..2....2..0..0..0..0..1..2....2..1..1..2..1..1..2

Crossrefs

Sequence in context: A078518 A234478 A130001 * A253754 A236779 A116228

Adjacent sequences: A253744 A253745 A253746 * A253748 A253749 A253750

Keyword

nonn

Author

R. H. Hardin, Jan 11 2015

Status

approved