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A295390 Number T(n,k) of permutations of [n] having exactly k consecutive 3-term arithmetic progressions; triangle T(n,k), n>=0, 0<=k<=max(n-2,0), read by rows.

%I A295390 #15 Nov 18 2020 09:32:20
%S A295390 1,1,2,4,2,18,4,2,80,34,4,2,482,196,36,4,2,3280,1418,292,44,4,2,26244,
%T A295390 11292,2426,304,48,4,2,231148,106132,22156,3010,372,56,4,2,2320130,
%U A295390 1046176,225804,32308,3892,424,60,4,2,25238348,11679626,2585080,366484,42176,4540,472,68,4,2
%N A295390 Number T(n,k) of permutations of [n] having exactly k consecutive 3-term arithmetic progressions; triangle T(n,k), n>=0, 0<=k<=max(n-2,0), read by rows.
%H A295390 Alois P. Heinz, <a href="/A295390/b295390.txt">Rows n = 0..18, flattened</a>
%H A295390 Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>
%H A295390 <a href="/index/No#non_averaging">Index entries related to non-averaging sequences</a>
%e A295390 Triangle T(n,k) begins:
%e A295390         1;
%e A295390         1;
%e A295390         2;
%e A295390         4,       2;
%e A295390        18,       4,      2;
%e A295390        80,      34,      4,     2;
%e A295390       482,     196,     36,     4,    2;
%e A295390      3280,    1418,    292,    44,    4,   2;
%e A295390     26244,   11292,   2426,   304,   48,   4,  2;
%e A295390    231148,  106132,  22156,  3010,  372,  56,  4, 2;
%e A295390   2320130, 1046176, 225804, 32308, 3892, 424, 60, 4, 2;
%e A295390   ...
%Y A295390 Column k=0 gives A295370.
%Y A295390 Row sums give A000142.
%Y A295390 Cf. A162982, A289207.
%K A295390 nonn,tabf
%O A295390 0,3
%A A295390 _Alois P. Heinz_, Nov 21 2017