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A321769 Consider the tree of triples P(n, k) with n > 0 and 0 < k <= 3^(n-1), such that P(1, 1) = [3; 4; 5] and each triple t on some row branches to the triples A*t, B*t, C*t on the next row (with A = [1, -2, 2; 2, -1, 2; 2, -2, 3], B = [1, 2, 2; 2, 1, 2; 2, 2, 3] and C = [-1, 2, 2; -2, 1, 2; -2, 2, 3]); T(n, k) is the second component of P(n, k). 7
4, 12, 20, 8, 24, 48, 28, 80, 120, 36, 56, 72, 12, 40, 88, 60, 208, 304, 84, 168, 224, 44, 176, 336, 180, 456, 696, 220, 288, 360, 52, 140, 252, 120, 252, 396, 136, 132, 156, 16, 60, 140, 104, 396, 572, 152, 340, 460, 96, 468, 884, 464, 1140, 1748, 560, 700 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The tree P runs uniquely through every primitive Pythagorean triple.

See A321768 for additional comments about P.

All terms are even.

LINKS

Rémy Sigrist, Rows n = 1..9, flattened

Wikipedia, Tree of primitive Pythagorean triples

Index entries related to Pythagorean Triples

FORMULA

Empirically:

- T(n, 1) = A046092(n),

- T(n, (3^(n-1) + 1)/2) = A046729(n),

- T(n, 3^(n-1)) = 4 * n.

EXAMPLE

The first rows are:

   4

   12, 20, 8

   24, 48, 28, 80, 120, 36, 56, 72, 12

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^(n-1)+k-1, 3)); for (i=2, #d, t = M[d[i]+1] * t); return (t[2, 1])

CROSSREFS

See A321768 and A321770 for the other components.

Cf. A046092, A046729.

Sequence in context: A240762 A050021 A239662 * A133096 A309085 A104814

Adjacent sequences:  A321766 A321767 A321768 * A321770 A321771 A321772

KEYWORD

nonn,tabf

AUTHOR

Rémy Sigrist, Nov 18 2018

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)