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

1,4

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

Links

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

Example

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

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 *)

Prog

(PARI) a(n) = binomial(n, n\2) % n; \\ Michel Marcus, May 14 2018
(Magma) [Binomial(n, Floor(n/2)) mod n: n in [1..110]]; // G. C. Greubel, Feb 17 2019
(Sage) [mod(binomial(n, floor(n/2)), n) for n in (1..110)] # G. C. Greubel, Feb 17 2019

Crossrefs

Cf. A001405, A020475.

Sequence in context: A327371 A037228 A002117 * A158327 A368707 A136581

Adjacent sequences: A042967 A042968 A042969 * A042971 A042972 A042973

Keyword

nonn,look

Author

Labos Elemer

Extensions

Name corrected by Jon E. Schoenfield, May 13 2018

Status

approved