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A090324 Second in a series of triangular arrays generating the natural numbers (cf. A079946). 2

%I #4 Mar 31 2012 13:23:37

%S 6,13,10,27,21,18,55,43,37,34,111,87,75,69,66,223,175,151,139,133,130,

%T 447,351,303,279,267,261,258,895,703,607,559,535,523,517,514

%N Second in a series of triangular arrays generating the natural numbers (cf. A079946).

%C Note that for each triangular array T(row+1,col) = 2 * T(row,col) +1 and that the change from T(row,col+1) to T(row,col) can be readily discerned. In the first array that pattern is 1 2 4 8 ...while in the second, it becomes 3 6 12 24 48 ... and in general, the pattern for the k-th array will begin with 2k-1.

%e The first array begins

%e 1

%e 3 2

%e 7 5 4

%e 15 11 9 8

%e 31 23 19 17 16

%e so a(1) begins with six. In general each triangular array will begin with

%e the next term from A079946.

%K easy,nonn,tabl

%O 1,1

%A _Alford Arnold_, Jan 26 2004

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