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A200984 Number of nX2 0..4 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%I A200984 #8 Jul 22 2025 16:02:46
%S A200984 10,10,20,79,21,226,157,227,678,120,1272,789,1015,2697,404,4232,2484,
%T A200984 3008,7496,1025,10650,6050,7060,16895,2181,22530,12525,14255,33174,
%U A200984 4116,42336,23177,25907,59073,7120,72992,39504,43560,97792,11529,117882,63234
%N A200984 Number of nX2 0..4 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
%C A200984 Column 2 of A200990
%H A200984 R. H. Hardin, <a href="/A200984/b200984.txt">Table of n, a(n) for n = 1..210</a>
%F A200984 Empirical: a(n) = 5*a(n-5) -10*a(n-10) +10*a(n-15) -5*a(n-20) +a(n-25)
%F A200984 Subsequences for n modulo 5 = 1,2,3,4,0:
%F A200984 p=(n+4)/5: a(n) = (115/6)*p^4 - 11*p^3 + (11/6)*p^2
%F A200984 q=(n+3)/5: a(n) = (115/12)*q^4 + (1/2)*q^3 - (1/12)*q^2
%F A200984 r=(n+2)/5: a(n) = (115/12)*r^4 + (49/6)*r^3 + (23/12)*r^2 + (1/3)*r
%F A200984 s=(n+1)/5: a(n) = (115/6)*s^4 + 35*s^3 + (125/6)*s^2 + 4*s
%F A200984 t=(n+0)/5: a(n) = (23/12)*t^4 + (37/6)*t^3 + (91/12)*t^2 + (13/3)*t + 1
%e A200984 Some solutions for n=3
%e A200984 ..0..1....0..2....0..1....0..3....0..2....0..1....0..1....0..2....0..2....0..2
%e A200984 ..1..2....1..3....2..3....1..3....1..3....0..3....0..2....1..3....0..3....1..3
%e A200984 ..3..4....4..4....2..4....2..4....2..4....2..4....3..4....3..4....1..4....1..4
%K A200984 nonn
%O A200984 1,1
%A A200984 _R. H. Hardin_ Nov 25 2011