A070764 - OEIS

A070764

Number of polyiamonds with n cells, with holes.

0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 25, 108, 450, 1713, 6267, 21988, 75185, 251590, 828408, 2692630, 8661287, 27624040, 87479663, 275392248, 862593661, 2690285608, 8359581585, 25893044920, 79978118632, 246433568617, 757696112134, 2325224420164, 7123627399429, 21791318924996, 66570286462599, 203119558522513, 619084154962394, 1885038245845679, 5734606563668062, 17431545733501175

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OFFSET

1,10

COMMENTS

The number of holes in a polyiamond can be calculated by the formula: H = A + 1 - s/2 where A is the area, s = A + Sum_{ i = 0..3 } (2-i)*E(i), and E(i) is the number of vertices adjacent to i groups of unoccupied cells in the triangular lattice. - John Mason, Sep 04 2025

LINKS

Table of n, a(n) for n=1..40.

Craig Knecht, Enneiamond with a hole - positions in a triangle.

Craig Knecht, Hexagon tiling.

Craig Knecht, Most equal distribution using the polyiamonds with holes.

Craig Knecht, Newton's Cradle.

Craig Knecht, Polyiamond 12-gon.

Craig Knecht, Tilings with fixed triangles in a frame.

CROSSREFS

Equals A000577 - A070765. Cf. A001419, A001420, A038144, A341630.

Sequence in context: A378407 A225692 A359524 * A327646 A244746 A110051

Adjacent sequences: A070761 A070762 A070763 * A070765 A070766 A070767