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Number of nX7 nonnegative integer arrays with upper left 0 and lower right n+7-4 and value increasing by 0 or 1 with every step right or down
2

%I #4 Dec 24 2014 08:16:03

%S 15,211,1948,12686,64920,277585,1030330,3407823,10237249,28340232,

%T 73128376,177500233,408299906,895580310,1882850350,3810729118,

%U 7452433875,14127861337,26034391284,46747817584,81967052716,140602733711

%N Number of nX7 nonnegative integer arrays with upper left 0 and lower right n+7-4 and value increasing by 0 or 1 with every step right or down

%C Column 7 of A252876

%H R. H. Hardin, <a href="/A252875/b252875.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/660441600)*n^14 + (1/9434880)*n^13 + (1/311850)*n^12 + (283/4989600)*n^11 + (23/34560)*n^10 + (5/896)*n^9 + (55843/1587600)*n^8 + (153793/907200)*n^7 + (4422487/7257600)*n^6 + (1152217/725760)*n^5 + (14953/4800)*n^4 + (834067/302400)*n^3 + (46071121/16816800)*n^2 - (359/17160)*n + 4

%e Some solutions for n=3

%e ..0..0..1..1..2..3..4....0..1..2..3..4..4..4....0..1..2..3..3..4..5

%e ..1..1..2..2..3..4..5....1..2..3..4..4..5..5....1..2..2..3..4..5..6

%e ..2..2..2..3..4..5..6....1..2..3..4..5..5..6....1..2..3..4..5..5..6

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 24 2014