A131636 List of impossible triples {V, F, E} that satisfy Euler's equation V=E-F+2 but do not correspond to polyhedra.

0, 2, 0, 0, 3, 1, 1, 1, 0, 1, 2, 1, 1, 3, 2, 2, 0, 0, 2, 1, 1, 2, 2, 2, 2, 3, 3, 3, 0, 1, 3, 1, 2, 3, 2, 3, 3, 3, 4

Offset

1,2

Comments

This set of triples seems to be a finite set of "graphs" that are Euler solutions but not polyhedra.

Links

Table of n, a(n) for n=1..39.

Formula

If V<4 and F<4 and E<7 and V=E-F+2: a(n) = {V(m),F(m),E(m)}

Mathematica

a = Delete[Union[Flatten[Table[If[v + f - 2 - e0 == 0, {v, f, e0}, {}], {v, 0, 3}, {f, 0, 3}, {e0, 0, 6}], 2]], 1]; Flatten[a]

Crossrefs

Cf. A130840.

Sequence in context: A351592 A082660 A134673 * A188023 A077888 A319668

Adjacent sequences: A131633 A131634 A131635 * A131637 A131638 A131639

Keyword

nonn

Author

Roger L. Bagula, Sep 05 2007

Extensions

Partially edited by N. J. A. Sloane, Sep 14 2007.

Status

approved