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A173302 Irregular triangle by rows, generated from an array with A000041 starting again at columns (2^n - 1), n=1,2,3,...

%I A173302 #8 Aug 10 2018 09:16:57
%S A173302 1,1,1,2,1,3,2,1,5,3,1,7,5,2,11,7,3,15,11,5,1,22,15,7,1,30,22,11,2,42,
%T A173302 30,15,3,56,42,22,5,77,56,30,7,101,77,42,11,135,101,56,15,176,135,77,
%U A173302 22,1,231,176,101,30,1,297,231,135,42,2
%N A173302 Irregular triangle by rows, generated from an array with A000041 starting again at columns (2^n - 1), n=1,2,3,...
%C A173302 Sum of finite difference terms of the array create triangle A173304.
%C A173302 Row sums = A173303.
%F A173302 Create an array with A000041 in row 0, then A000041 starts anew under successive columns (1, 3, 7, 15, 31,...). (Cf. A173301).
%F A173302 Columns of the array = rows of A173302.
%e A173302 The generating array =
%e A173302 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176,...
%e A173302 ...1, 1, 2, 3, 5,..7,.11, 15, 22, 30, 42, 56, .77, 101, 135,...
%e A173302 .........1, 1, 2,..3...5,..7, 11, 15, 22, 30, .42, .56, .77,...
%e A173302 .......................1,..1,..2,..3,..5,..7,..11,..15,..22,...
%e A173302 ..........................................................1,...
%e A173302 ...then columns become the rows of triangle A173302:
%e A173302 1;
%e A173302 1, 1;
%e A173302 2, 1;
%e A173302 3, 2, 1;
%e A173302 5, 3, 1;
%e A173302 7, 5, 2;
%e A173302 11, 7, 3;
%e A173302 15, 11, 5, 1;
%e A173302 22, 15, 7, 1;
%e A173302 30, 22, 11, 2;
%e A173302 42, 30, 15, 3;
%e A173302 56, 42, 22, 5;
%e A173302 77, 56, 30, 7;
%e A173302 101, 77, 4, 11;
%e A173302 135, 101, 56, 15;
%e A173302 176, 135, 77, 22, 1;
%e A173302 ...
%Y A173302 Cf. A000041, A173301, A173303, A173304.
%K A173302 nonn,tabf
%O A173302 0,4
%A A173302 _Gary W. Adamson_, Feb 15 2010