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%I #10 Apr 10 2016 23:23:50
%S 0,0,0,0,0,1,0,0,2,0,1,4,0,0,2,6,0,1,4,9,0,0,2,6,12,0,1,4,9,16,0,0,2,
%T 6,12,20,0,1,4,9,16,25,0,0,2,6,12,20,30,0,1,4,9,16,25,36,0,0,2,6,12,
%U 20,30,42,0,1,4,9,16,25,36,49
%N Irregular triangle read by rows: alternate (k-1)*k, k^2, for k = 0 to n.
%C This is the irregular triangle e(n) mentioned in A269837.
%C Last number: 0, 0, 0, 1, 2, 4, 6, 9, 12, 16, 20, 25, ... = A002620 with a third initial 0.
%C Row sums: 0, 0, 0, 1, 2, 5, 8, 14, 20, 30, 40, ... = A006918 with three initial 0.
%C Columns: the sum of the first two terms is A000384(n).
%e Irregular triangle:
%e 0,
%e 0,
%e 0, 0,
%e 0, 1,
%e 0, 0, 2,
%e 0, 1, 4,
%e 0, 0, 2, 6,
%e 0, 1, 4, 9,
%e 0, 0, 2, 6, 12,
%e 0, 1, 4, 9, 16,
%e 0, 0, 2, 6, 12, 20,
%e 0, 1, 4, 9, 16, 25,
%e etc.
%t Flatten[Transpose /@ Table[{k (k - 1), k^2}, {n, 0, 7}, {k, 0, n}]] (* _Michael De Vlieger_, Apr 10 2016 *)
%Y Cf. A000290, A000384, A002262, A006918, A161680, A269837.
%K nonn,tabf
%O 0,9
%A _Paul Curtz_, Apr 10 2016