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A256255 Triangle read by rows: T(n,k) = 6*k + 1, n>=0, 0<=k<=(2^n-1).

%I A256255 #21 Sep 26 2023 07:40:54
%S A256255 1,1,7,1,7,13,19,1,7,13,19,25,31,37,43,1,7,13,19,25,31,37,43,49,55,61,
%T A256255 67,73,79,85,91,1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,103,
%U A256255 109,115,121,127,133,139,145,151,157,163,169,175,181,187,1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,103
%N A256255 Triangle read by rows: T(n,k) = 6*k + 1, n>=0, 0<=k<=(2^n-1).
%C A256255 Row n lists the first 2^n terms of A016921, n >= 0.
%C A256255 Row sums give A165665.
%C A256255 Right border gives A048488.
%C A256255 The sum of all terms of the first k rows gives A060867(k).
%C A256255 The product of the terms of the third row is equal to the Hardy-Ramanujan number: 1 * 7 * 13 * 19 = 1729.
%H A256255 Paolo Xausa, <a href="/A256255/b256255.txt">Table of n, a(n) for n = 0..16382</a> (rows 0..13 of the triangle, flattened)
%e A256255 Triangle begins:
%e A256255 1;
%e A256255 1,7;
%e A256255 1,7,13,19;
%e A256255 1,7,13,19,25,31,37,43;
%e A256255 1,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91;
%e A256255 ...
%e A256255 Illustration of initial terms in the fourth quadrant of the square grid:
%e A256255 ------------------------------------------------------------------------
%e A256255 n   a(n)             Compact diagram
%e A256255 ------------------------------------------------------------------------
%e A256255 .            _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
%e A256255 0    1      |_|_  |_ _ _  |_ _ _ _ _ _ _  |
%e A256255 1    1      | |_| |_ _  | |_ _ _ _ _ _  | |
%e A256255 2    7      |_ _ _|_  | | |_ _ _ _ _  | | |
%e A256255 3    1      | | | |_| | | |_ _ _ _  | | | |
%e A256255 4    7      | | |_ _ _| | |_ _ _  | | | | |
%e A256255 5   13      | |_ _ _ _ _| |_ _  | | | | | |
%e A256255 6   19      |_ _ _ _ _ _ _|_  | | | | | | |
%e A256255 7    1      | | | | | | | |_| | | | | | | |
%e A256255 8    7      | | | | | | |_ _ _| | | | | | |
%e A256255 9   13      | | | | | |_ _ _ _ _| | | | | |
%e A256255 10  19      | | | | |_ _ _ _ _ _ _| | | | |
%e A256255 11  25      | | | |_ _ _ _ _ _ _ _ _| | | |
%e A256255 12  31      | | |_ _ _ _ _ _ _ _ _ _ _| | |
%e A256255 13  37      | |_ _ _ _ _ _ _ _ _ _ _ _ _| |
%e A256255 14  43      |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
%e A256255 .
%e A256255 a(n) is also the number of cells in the n-th region of the diagram.
%e A256255 For other diagrams of the same family see A241717 and A256258.
%t A256255 With[{rows=7},Array[Range[1,6*2^#,6]&,rows,0]] (* _Paolo Xausa_, Sep 26 2023 *)
%Y A256255 Cf. A000225, A001235, A016921, A048488, A060867, A165665, A241717, A256258.
%K A256255 nonn,tabf
%O A256255 0,3
%A A256255 _Omar E. Pol_, Apr 30 2015