

A321782


Triangle T(n, k) read by rows, n > 0 and 0 < k <= 3^(n1): T(n, k) = sqrt((A321768(n, k) + A321770(n, k))/2).


3



2, 3, 5, 4, 4, 8, 7, 8, 12, 9, 7, 9, 6, 5, 11, 10, 13, 19, 14, 12, 16, 11, 11, 21, 18, 19, 29, 22, 16, 20, 13, 10, 18, 15, 14, 22, 17, 11, 13, 8, 6, 14, 13, 18, 26, 19, 17, 23, 16, 18, 34, 29, 30, 46, 35, 25, 31, 20, 17, 31, 26, 25, 39, 30, 20, 24, 15, 14, 30
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OFFSET

1,1


COMMENTS

This sequence and A321783 are related to a parametrization of the primitive Pythagorean triples in the tree described in A321768.


LINKS

Rémy Sigrist, Rows n = 1..9, flattened
Index entries related to Pythagorean Triples


FORMULA

Empirically:
 T(n, 1) = n + 1,
 T(n, (3^(n1) + 1)/2) = A000129(n + 1),
 T(n, 3^(n1)) = 2 * n.


EXAMPLE

The first rows are:
2
3, 5, 4
4, 8, 7, 8, 12, 9, 7, 9, 6


PROG

(PARI) M = [[1, 2, 2; 2, 1, 2; 2, 2, 3], [1, 2, 2; 2, 1, 2; 2, 2, 3], [1, 2, 2; 2, 1, 2; 2, 2, 3]];
T(n, k) = my (t=[3; 4; 5], d=digits(3^(n1)+k1, 3)); for (i=2, #d, t = M[d[i]+1] * t); return (sqrtint((t[1, 1] + t[3, 1])/2))


CROSSREFS

Cf. A000129, A321768, A321770, A321783.
Sequence in context: A185332 A023818 A102149 * A104204 A131296 A267808
Adjacent sequences: A321779 A321780 A321781 * A321783 A321784 A321785


KEYWORD

nonn,tabf


AUTHOR

Rémy Sigrist, Nov 18 2018


STATUS

approved



