A235963 n appears (n+1)/(1 + (n mod 2)) times.

0, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13

Offset

0,3

Comments

n appears A001318(n+1) - A001318(n) = A026741(n+1) times.

Sum_{k=0...a(n)} (-1)^ceiling(k/2)*p(n-G(k)) = 0 for n>0, where p(n)=A000041(n) is the partition function, and G(k)=A001318(k) denotes the generalized pentagonal numbers.

Row lengths of A238442, n >= 1. - Omar E. Pol, Dec 22 2016

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Formula

Let t = (sqrt(n*8/3 + 1) - 1)/2 + 1/3 and let k = floor(t); then a(n) = 2k if t - k < 2/3, 2k+1 otherwise. - Jon E. Schoenfield, Jun 13 2017

Mathematica

Table[Table[n, {(n + 1)/(1 + Mod[n, 2])}], {n, 0, 14}]//Flatten (* T. D. Noe, Jan 29 2014 *)

Crossrefs

Cf. A000041, A001318, A026741, A238442.

Sequence in context: A367128 A028829 A130855 * A100196 A278078 A094708

Adjacent sequences: A235960 A235961 A235962 * A235964 A235965 A235966

Keyword

nonn

Author

Mircea Merca, Jan 17 2014

Status

approved