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%I #10 Apr 13 2016 00:14:56
%S 1,3,3,6,6,5,10,10,9,7,15,15,14,12,9,21,21,20,18,15,11,28,28,27,25,22,
%T 18,13,36,36,35,33,30,26,21,15,45,45,44,42,39,35,30,24,17,55,55,54,52,
%U 49,45,40,34,27,19,66,66,65,63,60,56,51,45,38,30,21
%N Triangle read by rows. The first column is A000217(n+1). From the second row we apply - A002262(n) for the following terms of the row.
%C Row sums: A084990(n+1).
%C A158405(n) = A002262(n) + A002260(n). See the formula.
%C (Without its first column, A094728 is A120070, which could be built from positive A005563 and -A158894.)
%F a(n) = A094728(n+1) - A049780(n).
%e a(0) = 1, a(1) = 3, a(2) =3-0 = 3, a(3) = 6, a(4) =6-0= 6, a(5) =6-1= 5, ... .
%e Triangle:
%e 1,
%e 3, 3,
%e 6, 6, 5,
%e 10, 10, 9, 7,
%e 15, 15, 14, 12, 9,
%e 21, 21, 20, 18, 15, 11,
%e 28, 28, 27, 25, 22, 18, 13,
%e 36, 36, 35, 33, 30, 26, 21, 15,
%e etc.
%t Table[(n^2 - n)/2 - Prepend[Accumulate@ Range[0, n - 3], 0], {n, 12}] // Flatten (* _Michael De Vlieger_, Apr 12 2016 *)
%Y Cf. A000096, A000217, A002260, A002262, A005408, A005563, A049780, A084990, A094728, A120070, A158405, A158894.
%K nonn,tabl
%O 0,2
%A _Paul Curtz_, Apr 12 2016
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