A202920 - OEIS

%I #5 Mar 31 2012 12:36:52

%S 1,20,534,11016,150590,1441046,10457226,61213311,302092215,1297497783,

%T 4965323693,17234628058,55015736433,163298076933,454724969302,

%U 1196643377731,2994141259048,7159760760474,16433842970073,36343144995894

%N Number of nX4 nonnegative integer arrays with each row and column increasing from zero by 0, 1, 2 or 3

%C Column 4 of A202924

%H R. H. Hardin, <a href="/A202920/b202920.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (14137/1600593426432000)*n^18 + (63821/118562476032000)*n^17 + (19169/1255367393280)*n^16 + (1403503/5230697472000)*n^15 + (92953/29113344000)*n^14 + (3605737/135862272000)*n^13 + (10145857/65840947200)*n^12 + (239478037/402361344000)*n^11 + (295677857/219469824000)*n^10 + (199871209/146313216000)*n^9 + (195277507/68976230400)*n^8 + (852272347/28740096000)*n^7 + (1232979942193/11769069312000)*n^6 + (100190391911/1307674368000)*n^5 - (2533465447/11887948800)*n^4 + (39976849/103194000)*n^3 + (221344693/200491200)*n^2 - (3054187/2042040)*n + 1

%e Some solutions for n=4

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

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

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

%e ..0..2..3..3....0..2..5..7....0..3..5..7....0..2..4..5....0..3..6..6

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 26 2011