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Triangle read by rows extracted from convolution product (1,2,3,...) * A002865: (1,1,2,2,4,4,7,8,...)
2

%I #3 Mar 30 2012 17:25:35

%S 1,1,2,2,2,3,2,4,3,4,4,4,6,4,5,4,8,6,8,5,6,7,8,12,8,10,6,7,8,14,12,16,

%T 10,12,7,8,8,14,12,16,10,12,7,8,12,16,21,16,20,12,14,8,9,14,24,24,28,

%U 20,24,14,10,9,10

%N Triangle read by rows extracted from convolution product (1,2,3,...) * A002865: (1,1,2,2,4,4,7,8,...)

%C Row sums = A058682 starting (1, 3, 7, 13, 23, 37, 58, 87,...).

%F Triangle read by rows, ascending diagonals of an array formed by the product of

%F (1,2,3,...) and (1,1,2,2,4,4,7,8,12,...).

%e The triangle = upward sloping diagonals of multiplication table:

%e .

%e 1,..2,..3,..4,..5,..6,..7,...

%e 1,..2,..3,..4,..5,..6,..7,...

%e 2,..4,..6,..8,.10,.12,.14,...

%e 2,..4,..6,..8,.10,.12,.14,...

%e ... First few rows of the triangle =

%e .

%e 1;

%e 1, 2;

%e 2, 2, 3;

%e 2, 4, 3, 4;

%e 4, 4, 6, 4, 5;

%e 4, 8, 6, 8, 5, 6;

%e 7, 8, 12, 8, 10, 6, 7;

%e 8, 14, 12, 16, 10, 12, 7, 8;

%e 12, 16, 21, 16, 20, 12, 14, 8, 9;

%e 14, 24, 24, 28, 20, 24, 14, 10, 9, 10;

%e 21, 28, 36, 32, 35, 24, 28, 16, 18, 10, 11;

%e 24, 42, 42, 48, 40, 42, 28, 32, 18, 20, 11, 12;

%e 34, 48, 63, 56, 60, 48, 49, 32, 36, 20, 22, 12, 13;

%e 41, 68, 72, 84, 70, 72, 56, 56, 36, 40, 22, 24, 13, 14;

%e ...

%Y Cf. A002865, A058682

%K nonn,tabl

%O 1,3

%A _Gary W. Adamson_, Dec 05 2009