A006482 Euler characteristics of polytopes. (Formerly M1357)

1, 1, 0, 2, 5, 9, 14, 20, 69, 125, 209, 329, 923, 1715, 3002, 5004, 12869, 24309, 43757, 75581, 184755, 352715, 646645, 1144065, 2704155, 5200299, 9657699, 17383859, 40116599

Offset

1,4

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..29.

H. Hadwiger and P. Mani, On polyhedra with extremal Euler characteristic, J. Combin. Theory, A 17 (1974), 345-349.

Formula

Numbers suggest that for n>3, a(n) = C(n, [n/2])-1 if (n mod 4)=0 or 1 and C(n, [n/2]-1)-1 otherwise. - Ralf Stephan, Jun 07 2005

Prog

(PARI) a(n)=if(n<3, (n==0||n==1), if(n<4, 2, -1+if(n%4==0||n%4==1, binomial(n, n\2), binomial(n, n\2-1)))) \\ Ralf Stephan, Jun 07 2005

Crossrefs

Sequence in context: A112873 A048093 A024669 * A191170 A191123 A152888

Adjacent sequences: A006479 A006480 A006481 * A006483 A006484 A006485

Keyword

nonn

Author

N. J. A. Sloane

Status

approved