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In the following square array numbers are entered like this a(1,1),a(1,2),a(2,1),a(3,1),a(2,2),a(1,3),a(1,4),a(2,3),a(3,2),a(4,1),a(5,1),a(4,2),... such that every entry is the geometric mean of the two diametrically opposite neighbors (wherever a pair exists). 1 2 4 8 16 32 64... 3 6 12 24 48 96 192... 9 18 36 72 144 288 576... 27 54 108 216 432 864 1728... ... Sequence contains numbers as they are entered.
1

%I #8 Dec 05 2013 19:56:04

%S 1,2,3,9,6,4,8,12,18,27,81,54,36,24,16,32,48,72,108,162

%N In the following square array numbers are entered like this a(1,1),a(1,2),a(2,1),a(3,1),a(2,2),a(1,3),a(1,4),a(2,3),a(3,2),a(4,1),a(5,1),a(4,2),... such that every entry is the geometric mean of the two diametrically opposite neighbors (wherever a pair exists). 1 2 4 8 16 32 64... 3 6 12 24 48 96 192... 9 18 36 72 144 288 576... 27 54 108 216 432 864 1728... ... Sequence contains numbers as they are entered.

%F a(r, s) = 3^(r-1)*2^(s-1).

%e In the following square array numbers are entered like this a(1,1), a(1,2), a(2,1), a(3,1), a(2,2), a(1,3), a(1,4), a(2,3), a(3,2), a(4,1), a(5,1), a(4,2),... such that every entry is the geometric mean of the two diametrically opposite neighbors (wherever a pair exists).

%e 1 2 4 8 16 32 64...

%e 3 6 12 24 48 96 192...

%e 9 18 36 72 144 288 576...

%e 27 54 108 216 432 864 1728...

%e ...

%e Sequence contains numbers as they are entered.

%Y Cf. A082233.

%K easy,nonn

%O 1,2

%A _Amarnath Murthy_, Apr 10 2003