A256436 Characteristic function of pentatope numbers.

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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

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.

Links

Antti Karttunen, Table of n, a(n) for n = 0..101270

Index entries for characteristic functions

Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See pp. 18, 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).

a(n) = 1 if n = binomial(floor((24*n)^(1/4))+2,4) and a(n) = 0 otherwise. - Chai Wah Wu, Sep 14 2025

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
(PARI) A256436(n) = for(i=3, oo, if(binomial(i, 4)>=n, return(binomial(i, 4)==n))); \\ Antti Karttunen, Dec 15 2024
(Python)
from math import comb, isqrt
def A256436(n): return int(n==comb(isqrt(isqrt(24*n))+2, 4)) # Chai Wah Wu, Sep 14 2025

Crossrefs

Cf. A000332 (pentatope numbers).

Sequence in context: A359456 A012245 A378454 * A253903 A255849 A379117

Adjacent sequences: A256433 A256434 A256435 * A256437 A256438 A256439

Keyword

nonn

Author

Mikael Aaltonen, Mar 29 2015

Extensions

More terms from Antti Karttunen, Dec 15 2024

Status

approved