A131481 -id:A131481 - cp's OEIS frontend

A130616 Number of triangular polyominoes (or polyiamonds) with perimeter at most n.

0, 0, 1, 2, 3, 7, 12, 28, 65, 185

Offset: 1

Tanya Khovanova, Aug 10 2007

Partial sums of A057729 - Number of triangular polyominoes (or polyiamonds) with perimeter n. a(n+2) >= A130867(n) - Triangular polyominoes (or polyiamonds) with n cells at most.

Cf. A131481 (number of n-cell polyiamonds with perimeter n+2).

Offset corrected by John Mason, Jan 16 2023

A131486 a(n) is the number of triangular polyominoes (polyiamonds) with n edges.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 1, 0, 3, 0, 4, 1, 11, 1, 23, 4, 62, 11, 150, 38, 411, 118, 1081, 389

Offset: 1

Tanya Khovanova, Jul 28 2007

An n-celled polyiamond with perimeter p has (3n+p)/2 edges. The maximum number of edges in an n-celled polyiamond is 2n+1.

Isoperimetrical Polyiamonds at Poly Pages

Cf. A000577: Triangular polyominoes (or polyiamonds) with n cells. A057729: Number of triangular polyominoes (or polyiamonds) [A000577] with perimeter n. A131481: a(n) is the number of n-cell polyiamonds (triangular polyominoes) with perimeter n+2.

A137191 Number of n-celled polyiamonds with perimeter < n+2.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 4, 11, 39, 120, 403, 1254, 4000, 12475, 39030

Offset: 1

Tanya Khovanova, Mar 03 2008

These are n-cell polyiamonds with the perimeter less than the maximum possible one.

If we associate a graph to a polyiamond with vertices representing cells and edges representing two cells with a common edge, then this sequence enumerates polyiamonds whose corresponding graphs have cycles.

A000577(n) - A131481(n)

cp's OEIS Frontend

A130616 Number of triangular polyominoes (or polyiamonds) with perimeter at most n.

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A131486 a(n) is the number of triangular polyominoes (polyiamonds) with n edges.

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A137191 Number of n-celled polyiamonds with perimeter < n+2.

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