A060754 Absolute values of a certain cubic form at integer points (see Formula).

1, 7, 8, 13, 27, 29, 41, 43, 49, 56, 64, 71, 83, 91, 97, 104, 113, 125, 127, 139, 167, 169, 181, 189, 197, 203, 211, 216, 223, 232, 239, 251, 281, 287, 293, 301, 307, 328, 337, 343, 344, 349, 351, 377, 379, 392, 419, 421, 433, 448, 449, 461, 463, 491, 497, 503

Offset

1,2

Comments

This sequence appears on p. 284 of Bryuno and Parusnikov, but the term 49 is missing. - Sean A. Irvine, Jul 31 2024

References

A. D. Bryuno and V. I. Parusnikov, Comparison of various generalizations of continued fractions, Mat. Zametki, 61 (No. 3, 1997), 339-348; English translation in Math. Notes, 61 (1997), 278-286.

Links

Table of n, a(n) for n=1..56.

Formula

{abs((L1.X)*(L2.X)*(L3.X)): X in Z^3} where "." denotes dot product and L1=(1,-c3,-1-c2), L2=(1,-c1,-1-c3), L3=(1,-c2,-1-c1) with c1=2*cos(6*Pi/7), c2=2*cos(4*Pi/7), c3=2*cos(2*Pi/7). - Sean A. Irvine, Jul 31 2024

Crossrefs

Sequence in context: A377332 A045765 A118068 * A196129 A286261 A136037

Adjacent sequences: A060751 A060752 A060753 * A060755 A060756 A060757

Keyword

nonn

Author

N. J. A. Sloane, Apr 24 2001

Extensions

Missing 49 and more terms from Sean A. Irvine, Jul 31 2024

Status

approved