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A224172 Number of n X 7 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A224172 #9 Mar 18 2025 20:55:38
%S A224172 1163,165212,5588411,91494280,1012166273,8857798353,65713691148,
%T A224172 426013124302,2451904991177,12667946702827,59314085710865,
%U A224172 253890734816827,1001536512782235,3667805164816918,12552963347081644,40389815158195689,122826907526807483,354709420054948952
%N A224172 Number of n X 7 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A224172 R. H. Hardin, <a href="/A224172/b224172.txt">Table of n, a(n) for n = 1..210</a>
%F A224172 Empirical: a(n) = (3642102403/12772735542927360000)*n^21 + (487469603/110586454917120000)*n^20 + (450670247/3723829604352000)*n^19 + (6552816539/4268249137152000)*n^18 + (623982887497/32011868528640000)*n^17 + (124732274921/627683696640000)*n^16 + (3648334363813/1977203644416000)*n^15 + (4680416798801/376610217984000)*n^14 + (87744827141299/807021895680000)*n^13 + (45260189845489/96566722560000)*n^12 + (11017436963867/2897001676800)*n^11 + (22454387742737/1755758592000)*n^10 + (3542239884149997071/39544072888320000)*n^9 + (18907698285363487/470762772480000)*n^8 + (47530133779063399/20175547392000)*n^7 - (24269518904069633/1743565824000)*n^6 + (49290543276442484369/666913927680000)*n^5 - (3320922257236141399/9262693440000)*n^4 + (126786352394209623343/123193822752000)*n^3 - (82401113278350059/48886437600)*n^2 + (143245612779559/10581480)*n - 54256709 for n>12.
%e A224172 Some solutions for n=3:
%e A224172 ..0..0..0..0..0..0..1....0..0..0..0..1..1..0....0..0..0..0..0..1..1
%e A224172 ..0..0..0..1..2..2..2....0..0..0..0..1..3..0....0..0..0..0..1..3..3
%e A224172 ..0..0..0..1..3..3..2....0..0..0..1..1..3..0....0..0..0..0..1..3..3
%Y A224172 Column 7 of A224173.
%K A224172 nonn
%O A224172 1,1
%A A224172 _R. H. Hardin_, Mar 31 2013
%E A224172 Name corrected by _Andrew Howroyd_, Mar 18 2025