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A341630 Number of fixed polyiamonds of area n without holes. 1
2, 3, 6, 14, 36, 94, 250, 675, 1832, 5005, 13746, 37901, 104902, 291312, 811346, 2265905, 6343854, 17801383, 50057400, 141034248, 398070362, 1125426581, 3186725646, 9036406687, 25658313188, 72946289247, 207628101578, 591622990214, 1687527542874, 4818113792640 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Equivalently, closed self-avoiding paths on the hexagonal net, where rotations and reflections of the whole path are not allowed and there is no selected starting point, with enclosed area n.
LINKS
Andrey Zabolotskiy, Table of n, a(n) for n = 1..60 (from Iwan Jensen's table)
Anthony J. Guttman, editor, Polygons, Polyominoes and Polycubes, LNP 775, Springer, 2009. See Table 16.8 "Triangular lattice SAP by area" on p. 476 with reference "Iwan Jensen, Unpublished".
CROSSREFS
Cf. A001420 (polyiamonds with holes allowed; first deviates at n=9), A036418 (polyiamonds with given perimeter, i.e. paths with given length), A070765 (free polyiamonds, i.e. reduced for symmetry: rotations and reflections are allowed), A006724 (analog for square lattice).
Sequence in context: A080408 A275774 A319323 * A001420 A337186 A049339
KEYWORD
nonn
AUTHOR
Andrey Zabolotskiy, Feb 16 2021
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)