A382195 -id:A382195 - cp's OEIS frontend

A382194 List of connected graphs that are squares, encoded as in A076184.

0, 1, 7, 31, 63, 239, 255, 511, 1023, 3455, 3887, 3951, 3967, 4095, 7679, 7903, 7935, 8191, 16350, 16351, 16383, 32767, 104063, 104447, 106287, 106351, 111587, 111599, 112511, 112623, 112639, 127791, 127855, 127871, 128879, 128895, 129023, 131071, 237567

Offset: 1

Pontus von Brömssen, Mar 18 2025

Intersection of A382193 and A382195.

			As an irregular triangle, where row n >= 1 contains A382180(n) terms:
     0;
     1;
     7;
    31,   63;
   239,  255,  511, 1023;
  3455, 3887, 3951, 3967, 4095, 7679, 7903, 7935, 8191, 16350, 16351, 16383, 32767;
  ...
The diamond graph is connected and isomorphic to the square of the path graph on 4 vertices. The code of the diamond graph is 31, so 31 is a term.

Pontus von Brömssen, Table of n, a(n) for n = 1..1580 (graphs on up to 9 vertices)
Eric Weisstein's World of Mathematics, Graph Square.
Wikipedia, Graph power.

Cf. A076184, A382180, A382193, A382195, A382283.

A382763 a(n) is the code (in the encoding given by A382754) of the square of the graph with code A382754(n).

Original entry on oeis.org

0, 1, 2, 3, 8, 9, 15, 15, 64, 65, 75, 127, 75, 76, 95, 127, 127, 127, 127, 1024, 1025, 1043, 1207, 2047, 1043, 1044, 1079, 1207, 1208, 1279, 2047, 1207, 1207, 1247, 1535, 1535, 2047, 2047, 2047, 1207, 1208, 1279, 1535, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047, 2047

Offset: 0

Pontus von Brömssen, Apr 05 2025

			As an irregular triangle, where row n >= 0 contains A000088(n) terms:
   0;
   1;
   2,  3;
   8,  9, 15,  15;
  64, 65, 75, 127, 75, 76, 95, 127, 127, 127, 127;
  ...

Cf. A000088, A382195, A382754, A382761, A382764.

a(n) = A382754(A382764(n)).

A382764 a(n) is the index in A382754 of the square of the graph with code A382754(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 7, 8, 9, 12, 18, 12, 13, 17, 18, 18, 18, 18, 19, 20, 24, 39, 52, 24, 25, 32, 39, 40, 49, 52, 39, 39, 47, 51, 51, 52, 52, 52, 39, 40, 49, 51, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52

Offset: 0

Pontus von Brömssen, Apr 05 2025

			As an irregular triangle, where row n >= 0 contains A000088(n) terms:
  0;
  1;
  2, 3;
  4, 5,  7,  7;
  8, 9, 12, 18, 12, 13, 17, 18, 18, 18, 18;
  ...

Cf. A000088, A382195, A382754, A382762, A382763.

cp's OEIS Frontend

A382194 List of connected graphs that are squares, encoded as in A076184.

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A382763 a(n) is the code (in the encoding given by A382754) of the square of the graph with code A382754(n).

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Formula

A382764 a(n) is the index in A382754 of the square of the graph with code A382754(n).

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