Douglas J. Durian - cp's OEIS frontend

A292150 Number of distinct convex octagons that can be formed from n congruent isosceles right triangles. Reflections are not counted as distinct.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 3, 0, 1, 1, 1, 1, 1, 1, 5, 0, 3, 1, 1, 1, 3, 3, 5, 1, 1, 2, 8, 1, 3, 2, 7, 3, 3, 5, 4, 2, 8, 3, 12, 2, 4, 7, 7, 3, 6, 6, 15, 3, 5, 8, 12, 7, 9, 5, 15, 4, 12, 11, 11, 7, 6

Offset: 1

Douglas J. Durian, Sep 13 2017

nonn

Illustrated with other convex polyabolos in A245676.

			The smallest convex octagonal polyabolos are for n = 14 and n = 20; both are symmetrical.

Douglas J. Durian, Table of n, a(n) for n = 1..750

Strictly less than A245676.

a(33) and beyond from Douglas J. Durian, Jan 25 2020

A292149 Number of distinct convex heptagons that can be formed from n congruent isosceles right triangles. Reflections are not counted as distinct.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 1, 3, 2, 1, 3, 2, 3, 1, 4, 6, 3, 3, 3, 3, 8, 1, 8, 11, 3, 4, 5, 8, 9, 5, 11, 8, 11, 6, 10, 13, 8, 9, 11, 17, 13, 6, 14, 11, 21, 8, 15, 25, 13, 12, 17, 20, 22, 12, 18, 24, 22, 13, 27, 27

Offset: 1

Douglas J. Durian, Sep 13 2017

nonn

Illustrated with other convex polyabolos in A245676.

			The smallest convex heptagonal polyabolos are for n = 15 (symmetrical) and n = 17 (asymmetrical).

Douglas J. Durian, Table of n, a(n) for n = 1..750

Strictly less than A245676.

a(33) and beyond from Douglas J. Durian, Jan 25 2020

A292148 Number of distinct convex hexagons that can be formed from n congruent isosceles right triangles. Reflections are not counted as distinct.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 1, 1, 3, 1, 2, 2, 4, 1, 4, 2, 6, 5, 5, 5, 10, 2, 6, 6, 8, 8, 10, 7, 14, 7, 10, 6, 13, 12, 12, 13, 19, 8, 16, 6, 15, 22, 17, 16, 25, 9, 16, 10, 23, 21, 22, 18, 27, 23, 18, 16, 29, 21, 29, 20, 35, 18, 27, 18, 23, 39, 28, 24, 43, 21, 32, 19

Offset: 1

Douglas J. Durian, Sep 13 2017

nonn

Illustrated with other convex polyabolos in A245676.

			The smallest convex hexagonal polyabolo that is asymmetric is for n = 9.

Douglas J. Durian, Table of n, a(n) for n = 1..750

Strictly less than A245676.

a(33) and beyond from Douglas J. Durian, Jan 24 2020

A292147 Number of distinct convex pentagons that can be formed from n congruent isosceles right triangles. Reflections are not counted as distinct.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 4, 1, 3, 5, 5, 2, 3, 2, 6, 5, 2, 8, 11, 1, 3, 7, 6, 7, 6, 7, 13, 7, 4, 8, 8, 5, 5, 13, 14, 8, 8, 4, 8, 14, 5, 17, 22, 5, 5, 7, 8, 14, 8, 14, 18, 13, 4, 11, 18, 7, 10, 22, 18, 15, 7, 9, 10, 19, 9, 16, 29, 8, 9, 12, 10, 23, 9, 19

Offset: 1

Douglas J. Durian, Sep 10 2017

nonn

Illustrated with other convex polyabolos in A245676.

			The smallest convex pentagonal polyabolo is for n=5.

Douglas J. Durian, Table of n, a(n) for n = 1..750

Strictly less than A245676.

a(33) and beyond from Douglas J. Durian, Jan 24 2020

A292146 Number of different convex quadrilaterals that can be formed from n congruent isosceles right triangles. Reflections are not counted as different.

Original entry on oeis.org

0, 2, 2, 5, 2, 5, 3, 9, 2, 5, 2, 11, 2, 6, 4, 13, 3, 7, 2, 11, 4, 5, 3, 19, 2, 5, 4, 12, 2, 10, 3, 17, 4, 6, 4, 16, 2, 5, 4, 19, 3, 10, 2, 11, 6, 6, 3, 27, 3, 7, 4, 11, 2, 10, 4, 20, 4, 5, 2, 22, 2, 6, 7, 21, 4, 10, 2, 12, 4, 10, 3, 28, 3, 5, 6, 11, 4, 10

Offset: 1

Douglas J. Durian, Sep 09 2017

nonn

Illustrated with other convex polyabolos in A245676.

			For n=2, there is a square and a parallelogram.

Andrew Howroyd, Table of n, a(n) for n = 1..1000
Andrew Howroyd, Convex Quadrilaterals formed from Polyabolos

Strictly less than A245676.

\\ here b is A100073
b(n) = if(n%2, floor(numdiv(n)/2), if(n%4, 0, floor(numdiv(n/4)/2)));
d(n) = my(t); sum(k=1, floor(sqrt((n-1)/2)), issquare(n+2*k^2,&t) && t>2*k);
a(n) = 2*b(n) + d(n) + if(n%2, 0, 2*numdiv(n/2) + b(n/2)) + if(n%4, 0, ceil(numdiv(n/4)/2)); \\ Andrew Howroyd, Sep 16 2017

Terms a(33) and beyond from Andrew Howroyd, Sep 16 2017

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User: Douglas J. Durian

A292150 Number of distinct convex octagons that can be formed from n congruent isosceles right triangles. Reflections are not counted as distinct.

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A292149 Number of distinct convex heptagons that can be formed from n congruent isosceles right triangles. Reflections are not counted as distinct.

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A292148 Number of distinct convex hexagons that can be formed from n congruent isosceles right triangles. Reflections are not counted as distinct.

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Examples

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A292147 Number of distinct convex pentagons that can be formed from n congruent isosceles right triangles. Reflections are not counted as distinct.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A292146 Number of different convex quadrilaterals that can be formed from n congruent isosceles right triangles. Reflections are not counted as different.

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Author

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PARI

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