A277561 a(n) = Sum_{k=0..n} ({binomial(n+2k,2k)*binomial(n,k)} mod 2).

1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 4, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 4, 4, 2, 4, 4, 4, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 4, 4, 4, 8, 8, 8, 4, 8, 4, 4, 2, 4, 4, 4, 4, 8, 4, 4, 2, 4, 4, 4, 2, 4, 2, 2, 2, 4, 4, 4, 4, 8, 4, 4, 4, 8, 8, 8, 4, 8, 4, 4, 4, 8, 8, 8, 8, 16, 8

Offset

0,2

Comments

Equals the run length transform of A040000: 1,2,2,2,2,2,...

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Chai Wah Wu, Sums of products of binomial coefficients mod 2 and run length transforms of sequences, arXiv:1610.06166 [math.CO], 2016.

Index entries for sequences computed with run length transform

Formula

a(n) = 2^A069010(n). a(2n) = a(n), a(4n+1) = 2a(n), a(4n+3) = a(2n+1). - Chai Wah Wu, Nov 04 2016

a(n) = A034444(A005940(1+n)). - Antti Karttunen, May 29 2017

Mathematica

Table[Sum[Mod[Binomial[n + 2 k, 2 k] Binomial[n, k], 2], {k, 0, n}], {n, 0, 86}] (* Michael De Vlieger, Oct 21 2016 *)

Prog

(Python)
def A277561(n):
    return sum(int(not (~(n+2*k) & 2*k) | (~n & k)) for k in range(n+1))
(PARI) a(n) = sum(k=0, n, binomial(n+2*k, 2*k)*binomial(n, k) % 2); \\ Michel Marcus, Oct 21 2016

Crossrefs

Cf. A005940, A034444, A040000, A069010, A106737.

Sequence in context: A183095 A304817 A242802 * A317684 A127973 A300654

Adjacent sequences: A277558 A277559 A277560 * A277562 A277563 A277564

Keyword

nonn

Author

Chai Wah Wu, Oct 19 2016

Status

approved