A309255 a(n) = n + 1 - Sum_{k=0..n} (Stirling1(n,k) mod 2).

0, 1, 1, 2, 3, 4, 3, 4, 7, 8, 7, 8, 9, 10, 7, 8, 15, 16, 15, 16, 17, 18, 15, 16, 21, 22, 19, 20, 21, 22, 15, 16, 31, 32, 31, 32, 33, 34, 31, 32, 37, 38, 35, 36, 37, 38, 31, 32, 45, 46, 43, 44, 45, 46, 39, 40, 49, 50, 43, 44, 45, 46, 31, 32, 63, 64, 63, 64, 65, 66, 63, 64, 69, 70, 67, 68, 69

Offset

0,4

Comments

Number of even entries in n-th row of triangle of Stirling numbers of the first kind (A048994).

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

G.f.: 1/(1 - x)^2 - (1 + x) * Product_{k>=0} (1 + 2*x^(2^(k+1))).

a(n) = n + 1 - 2^A000120(floor(n/2)).

Mathematica

Table[n + 1 - Sum[Mod[StirlingS1[n, k], 2], {k, 0, n}], {n, 0, 76}]
nmax = 76; CoefficientList[Series[1/(1 - x)^2 - (1 + x) Product[(1 + 2 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Prog

(PARI) a(n) = n + 1 - sum(k=0, n, stirling(n, k, 1) % 2); \\ Michel Marcus, Jul 19 2019
(PARI) a(n) = n + 1 - 2^hammingweight(n\2); \\ Amiram Eldar, Jul 25 2023

Crossrefs

Cf. A000120, A048967, A048994, A060632, A309256.

Sequence in context: A360379 A253852 A103672 * A375290 A201443 A291762

Adjacent sequences: A309252 A309253 A309254 * A309256 A309257 A309258

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 19 2019

Status

approved