A051556 - OEIS

A051556

a(n) = number of 0<=k<=n such that n+k divides binomial(n,k).

1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 6, 3, 1, 2, 2, 1, 3, 2, 3, 6, 2, 3, 5, 5, 2, 3, 6, 4, 6, 5, 10, 12, 6, 4, 10, 8, 3, 8, 5, 8, 5, 3, 5, 11, 4, 4, 10, 7, 8, 9, 19, 21, 12, 8, 7, 8, 4, 3, 17, 13, 19, 23, 10, 11, 13, 16, 18, 14, 9, 11, 19, 13, 9, 16, 16, 25, 21, 17, 15, 18, 13, 16, 17, 19

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OFFSET

1,9

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

For n=9, 0<=k<=n, n+k divides C(n,k) only when k=3 and k=5, so a(9)=2.

MAPLE

f:= proc(n)

nops(select(t -> binomial(n, t) mod (n+t) = 0, [$0..n]))

end proc:

map(f, [$1..100]); # Robert Israel, Feb 27 2024

MATHEMATICA

A051556[n_] := Count[Divisible[Binomial[n, Range[0, n]], Range[n, 2*n]], True];

Array[A051556, 100] (* Paolo Xausa, Feb 29 2024 *)

PROG

(PARI) a(n) = sum(k=0, n, (binomial(n, k) % (n+k)) == 0); \\ Michel Marcus, May 18 2014

CROSSREFS

Cf. A051574 (similar definition).

Sequence in context: A286135 A375010 A142475 * A330166 A081602 A077267

Adjacent sequences: A051553 A051554 A051555 * A051557 A051558 A051559

KEYWORD

nonn

AUTHOR

Leroy Quet

STATUS

approved