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A224283 Number of 4Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

%I A224283 #6 Jul 23 2025 05:04:40
%S A224283 256,16000,186516,1334973,8073038,44901359,233090092,1121852243,
%T A224283 4979825221,20391024279,77331512406,273217833082,905042600151,
%U A224283 2828381836611,8387049692461,23720147714267,64273739402314
%N A224283 Number of 4Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
%C A224283 Row 4 of A224281
%H A224283 R. H. Hardin, <a href="/A224283/b224283.txt">Table of n, a(n) for n = 1..210</a>
%F A224283 Empirical: a(n) = (1/2906843957821440000)*n^24 + (1/80745665495040000)*n^23 + (46391/53523844179886080000)*n^22 + (11257/405483668029440000)*n^21 + (1330123/1390229718958080000)*n^20 + (8502743/347557429739520000)*n^19 + (35671/59779399680000)*n^18 + (133834769/10670622842880000)*n^17 + (7571063047/30128817438720000)*n^16 + (2965237343/836911595520000)*n^15 + (328422846067/15064408719360000)*n^14 + (22514281381/48910417920000)*n^13 + (7036550185081/2254537359360000)*n^12 - (105103493973601/2510734786560000)*n^11 + (1257210817095943/1076029194240000)*n^10 - (236735071681049/19615115520000)*n^9 + (3534310707922188979/32011868528640000)*n^8 - (767055210116438233/1143281018880000)*n^7 + (10350657608308971137/3103191336960000)*n^6 - (8154723578394294443/703964701440000)*n^5 + (16475873524529520931/527973526080000)*n^4 - (482012437494247/8888443200)*n^3 + (78892730856408401/873054262080)*n^2 - (77283877096589/243374040)*n + 643573 for n>7
%e A224283 Some solutions for n=3
%e A224283 ..0..0..0....0..0..2....3..2..1....2..0..0....3..0..0....1..2..1....2..0..0
%e A224283 ..0..0..1....2..2..2....3..2..1....3..2..0....1..3..2....3..2..1....1..1..0
%e A224283 ..2..1..0....2..2..2....3..1..1....2..0..0....3..3..1....3..1..1....1..1..1
%e A224283 ..1..0..0....3..2..2....1..2..1....2..1..0....3..3..0....1..3..1....1..2..1
%K A224283 nonn
%O A224283 1,1
%A A224283 _R. H. Hardin_ Apr 02 2013