A220487 - OEIS

%I #10 Mar 05 2013 21:00:50

%S 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 55,57,59,60,61,62,63,64,65,66,69,74,76,80,87,90,92,94,95,96,97,98,99,

%U 100,101,102,103,104,105,107,111,113,116,122,125,127,129,134,138

%N Partial sums of triangle A206437.

%F a(A182181(n)) = A182244(n), n >= 1.

%F a(A006128(n)) = A066186(n), n >= 1.

%e 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 1;

%e 3, 4;

%e 7, 8, 9;

%e 11;

%e 15,17,18,19,20;

%e 23;

%e 28,30,31,32,33,34,35;

%e 37;

%e 41,43;

%e 46;

%e 52,55,57,59,60,61,62,63,64,65,66;

%e 69;

%e 74,76;

%e 80;

%e 87,90,92,94,95,96,97,98,99,100,101,102,103,104,105;

%e ...

%e 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 1;

%e 3, 4;

%e 7, 8, 9;

%e 11,15,17,18,19,20;

%e 23,28,30,31,32,33,34,35;

%e 37,41,43,46,52,55,57,59,60,61,62,63,64,65,66;

%e 69,74,76,80,87,90,92,94,95,96,97,98,99,100,101,102,103,104,105;

%e ...

%Y Cf. A000041, A006128, A066186, A135010, A138137, A138879, A141285, A182181, A182244, A186412, A194446, A206437.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Jan 18 2013