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A220487 Partial sums of triangle A206437.

%I A220487 #10 Mar 05 2013 21:00:50
%S A220487 1,3,4,7,8,9,11,15,17,18,19,20,23,28,30,31,32,33,34,35,37,41,43,46,52,
%T A220487 55,57,59,60,61,62,63,64,65,66,69,74,76,80,87,90,92,94,95,96,97,98,99,
%U A220487 100,101,102,103,104,105,107,111,113,116,122,125,127,129,134,138
%N A220487 Partial sums of triangle A206437.
%F A220487 a(A182181(n)) = A182244(n), n >= 1.
%F A220487 a(A006128(n)) = A066186(n), n >= 1.
%e A220487 When written as an irregular triangle in which row j has length A194446(j) then the right border gives A182244. Also the records of row lengths give the partition numbers (A000041) of the positive integers as shown below:
%e A220487 1;
%e A220487 3, 4;
%e A220487 7, 8, 9;
%e A220487 11;
%e A220487 15,17,18,19,20;
%e A220487 23;
%e A220487 28,30,31,32,33,34,35;
%e A220487 37;
%e A220487 41,43;
%e A220487 46;
%e A220487 52,55,57,59,60,61,62,63,64,65,66;
%e A220487 69;
%e A220487 74,76;
%e A220487 80;
%e A220487 87,90,92,94,95,96,97,98,99,100,101,102,103,104,105;
%e A220487 ...
%e A220487 Also when written as an irregular triangle in which row j has length A138137(j) then the right border gives A066186 as shown below:
%e A220487 1;
%e A220487 3, 4;
%e A220487 7, 8, 9;
%e A220487 11,15,17,18,19,20;
%e A220487 23,28,30,31,32,33,34,35;
%e A220487 37,41,43,46,52,55,57,59,60,61,62,63,64,65,66;
%e A220487 69,74,76,80,87,90,92,94,95,96,97,98,99,100,101,102,103,104,105;
%e A220487 ...
%Y A220487 Cf. A000041, A006128, A066186, A135010, A138137, A138879, A141285, A182181, A182244, A186412, A194446, A206437.
%K A220487 nonn,tabf
%O A220487 1,2
%A A220487 _Omar E. Pol_, Jan 18 2013