A307239 - OEIS

%I #19 Apr 05 2019 09:30:26

%S 1,1,1,1,2,1,1,3,3,1,1,2,6,2,1,1,3,2,2,3,1,1,2,5,2,5,2,1,1,3,7,7,7,7,

%T 3,1,1,2,10,14,14,14,10,2,1,1,3,6,6,14,14,6,6,3,1,1,2,3,6,10,14,10,6,

%U 3,2,1,1,3,5,3,2,6,6,2,3,5,3,1,1,2,2,2,5,2,6,2,5,2,2,2,1

%N Analog of Pascal's triangle, with A007947 applied to each sum.

%C The parity of the terms in this triangle is the same as in Pascal's triangle (A007318). As a consequence, the number of odd terms in row n is A001316(n).

%C The distribution of the terms different from 2 in the triangle evokes Sierpinski's triangle; this is also the case for terms that are multiples of 3 (see illustrations in Links section).

%H Rémy Sigrist, <a href="/A307239/a307239.png">Colored representation of the first 1500 rows</a> (where the color is function of log(T(n,k)))

%H Rémy Sigrist, <a href="/A307239/a307239_1.png">Representation of the 2's in the first 1500 rows</a> (black pixels correspond to 2's)

%H Rémy Sigrist, <a href="/A307239/a307239_2.png">Representation of the multiples of 3 in the first 1500 rows</a> (black pixels correspond to multiples of 3)

%e Triangle begins:

%e   0:                       1

%e   1:                     1   1

%e   2:                   1   2   1

%e   3:                 1   3   3   1

%e   4:               1   2   6   2   1

%e   5:             1   3   2   2   3   1

%e   6:           1   2   5   2   5   2   1

%e   7:         1   3   7   7   7   7   3   1

%e   8:       1   2  10  14  14  14  10   2   1

%e   9:     1   3   6   6  14  14   6   6   3   1

%e   ...

%o (PARI) rad(n) = my (p=factor(n)[,1]~); prod(i=1, #p, p[i])

%o { for (r=0, 12, row = vector(r+1, k, if ( k==1||k==r+1, 1, rad(row[k-1]+row[k]))); for (c=1, #row, print1 (row[c] ", "))) }

%Y Cf. A001316, A007318, A007947, A080396, A307356 (number of 2's in rows).

%K nonn,tabl

%O 0,5

%A _Rémy Sigrist_, Apr 01 2019