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A379998 Irregular triangle read by rows: T(n,k) is number of sequences of length k over {0,1,...,n-1} containing no two consecutive blocks with the same average, n >= 1, 0 <= k <= A379914(n).

%I A379998 #9 Jan 09 2025 09:07:55
%S A379998 1,1,1,2,2,2,1,3,6,8,1,4,12,28,38,50,24,6,1,5,20,64,148,316,370,340,
%T A379998 152,38,1,6,30,126,406,1142,2142,3380,4022,3910,2794,2048,988,496,234,
%U A379998 82,14,10,4,2,1,7,42,216,898,3314,9014,21760,41026,63898,78204,87820,71434,53984,34232,16716,6400,2346,644,148,12
%N A379998 Irregular triangle read by rows: T(n,k) is number of sequences of length k over {0,1,...,n-1} containing no two consecutive blocks with the same average, n >= 1, 0 <= k <= A379914(n).
%C A379998 See A379914 for details.
%C A379998 A sequence, its reversal, and its complement (where all terms x are replaced by n-1-x) are all counted.
%H A379998 Pontus von Brömssen, <a href="/A379998/b379998.txt">Table of n, a(n) for n = 1..139 (rows 1..9)</a>
%F A379998 T(n,0) = 1.
%F A379998 T(n,1) = n.
%F A379998 T(n,2) = n*(n-1) for n >= 2.
%F A379998 T(n,3) = A245996(n-1) for n >= 2.
%F A379998 Empirically: T(n,4) = T(n-1,4) + T(n-2,4) - T(n-5,4) - T(n-6,4) - T(n-7,4) + T(n-8,4) + T(n-9,4) + T(n-10,4) - T(n-13,4) - T(n-14,4) + T(n-15,4) for n >= 19.
%e A379998 Triangle begins:
%e A379998   1, 1;
%e A379998   1, 2,  2,  2;
%e A379998   1, 3,  6,  8;
%e A379998   1, 4, 12, 28,  38,  50,  24,   6;
%e A379998   1, 5, 20, 64, 148, 316, 370, 340, 152, 38;
%e A379998   ...
%Y A379998 Cf. A245996, A379914, A379999, A380000.
%K A379998 nonn,tabf
%O A379998 1,4
%A A379998 _Pontus von Brömssen_, Jan 09 2025