A190310 -id:A190310

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A190309

Number of acute isosceles triangles, distinct up to congruence, on an n X n grid (or geoboard).

+10
2

0, 0, 2, 5, 11, 19, 29, 40, 58, 74, 94, 113, 141, 168, 201, 227, 267, 304, 348, 390, 438, 483, 537, 590, 657, 709, 776, 837, 913, 979, 1057, 1130, 1225, 1299, 1396, 1472, 1576, 1663, 1768, 1863, 1974

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..41.

Eric Weisstein's World of Mathematics, Geoboard.

Eric Weisstein's World of Mathematics, Acute Triangle.

Eric Weisstein's World of Mathematics, Isosceles Triangle.

FORMULA

a(n) = A189978(n) - A190310(n) - A108279(n).

CROSSREFS

Cf. A028419, A108279, A189978, A190021, A190310.

KEYWORD

nonn

AUTHOR

Martin Renner, May 08 2011

STATUS

approved

A241239

Number of obtuse isosceles triangles, distinct up to congruence, on a centered hexagonal grid of size n.

+10
1

0, 1, 4, 10, 19, 30, 45, 61, 84, 106, 134, 165, 199, 234, 277, 321, 364, 412, 478, 523, 595

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

LINKS

Table of n, a(n) for n=1..21.

Eric Weisstein's World of Mathematics, Hex Number.

Eric Weisstein's World of Mathematics, Obtuse Triangle.

Eric Weisstein's World of Mathematics, Isosceles Triangle.

FORMULA

a(n) = A241237(n) - A241238(n).

EXAMPLE

For n = 2 the only kind of non-congruent obtuse isosceles triangles is the following:

/* *

. . *

\. .

CROSSREFS

Cf. A190310, A241230.

KEYWORD

nonn,more

AUTHOR

Martin Renner, Apr 17 2014

EXTENSIONS

a(7) from Martin Renner, May 31 2014

a(8)-a(21) from Giovanni Resta, May 31 2014

STATUS

approved

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