login
A256436
Characteristic function of pentatope numbers.
0
1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0
COMMENTS
The pentatope is also called the regular 4-simplex, pentachoron, 5-cell or 4-hypertetrahedron.
Pentatope numbers are of the form n*(n+1)*(n+2)*(n+3)/24.
FORMULA
For n > 0, a(n) = floor(sqrt( 4*sqrt( 24*n + 1) + 5 )/2 - 3/2) - floor(sqrt( 4*sqrt( 24*(n-1) + 1) + 5 )/2 - 3/2).
MATHEMATICA
Module[{nn=10, pent}, pent=Table[n(n+1)(n+2)(n+3)/24, {n, 0, nn}]; Table[If[MemberQ[pent, k], 1, 0], {k, 0, 120}]] (* Harvey P. Dale, Jul 18 2024 *)
PROG
(Magma) [1] cat [Floor(Sqrt(4*Sqrt(24*n+1)+5 )/2-3/2)-Floor(Sqrt(4*Sqrt(24*(n-1)+1)+5)/2-3/2): n in [1..100] ]; // Vincenzo Librandi, Mar 30 2015
CROSSREFS
Cf. A000332 (pentatope numbers).
Sequence in context: A094875 A359456 A012245 * A253903 A255849 A185059
KEYWORD
nonn
AUTHOR
Mikael Aaltonen, Mar 29 2015
STATUS
approved