A042970 a(n) = binomial(n, floor(n/2)) mod n.

0, 0, 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 2, 0, 6, 0, 2, 0, 16, 0, 2, 0, 4, 0, 2, 0, 20, 0, 0, 0, 6, 0, 2, 0, 24, 0, 2, 0, 20, 0, 6, 0, 28, 0, 2, 0, 12, 0, 2, 0, 32, 0, 20, 0, 0, 0, 2, 0, 4, 0, 2, 0, 6, 0, 42, 0, 40, 0, 42, 0, 52, 0, 2, 0, 44, 0, 20, 0, 20, 0, 2, 0, 0, 0, 2, 0, 48, 0, 0, 0, 52, 0, 2, 0

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• look

Comments

Value 924 occurs for 248 times among the first 20000 terms (see the horizontal stripe near y=1000 in the scatter plot). Where does it originate from? - Antti Karttunen, Feb 13 2019

Examples

			a(10) = binomial(10,5) mod 10 = 252 mod 10 = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001405, A020475.

Programs

Magma

[Binomial(n, Floor(n/2)) mod n: n in [1..110]]; // G. C. Greubel, Feb 17 2019

Maple

a:=n->modp(binomial(n,floor(n/2)),n): seq(a(n),n=1..110); # Muniru A Asiru, Feb 17 2019

Mathematica

Table[Mod[Binomial[n, Floor[n/2]], n], {n,1,110}] (* G. C. Greubel, Feb 17 2019 *)

PARI

a(n) = binomial(n, n\2) % n; \\ Michel Marcus, May 14 2018

Sage

[mod(binomial(n,floor(n/2)), n) for n in (1..110)] # G. C. Greubel, Feb 17 2019

Extensions

Name corrected by Jon E. Schoenfield, May 13 2018