

A004273


0 together with odd numbers.


34



0, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131
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OFFSET

0,3


COMMENTS

For n >= 1, a(n) = numbers k such that arithmetic mean of the first k positive integers is integer. A040001(a(n)) = 1. See A145051 and A040001.
For n >= 1, a(n) = corresponding values of antiharmonic means to numbers from A016777 (numbers k such that antiharmonic mean of the first k positive integers is integer).
If the nth prime is denoted by p(n) then it appears that a(j) = distinct, increasing values of (Sum of the quadratic nonresidues of p(n)  Sum of the quadratic residues of p(n)) / p(n) for each j.  Christopher Hunt Gribble, Oct 05 2010
Dimension of the space of weight 2n+2 cusp forms for Gamma_0(6).
The size of a maximal 2degenerate graph of order n1 (this class includes 2trees and maximal outerplanar graphs (MOPs)).  Allan Bickle, Nov 14 2021


LINKS



FORMULA

a(n) = 2*n  ((n+2) mod (n+1)), n >= 0.  Paolo P. Lava, Aug 29 2007
Euler transform of length 2 sequence [3, 1].  Michael Somos, Jul 03 2014
a(n) = (4*n  1  (1)^(2^n))/2.  Luce ETIENNE, Jul 11 2015


EXAMPLE

G.f. = x + 3*x^2 + 5*x^3 + 7*x^4 + 9*x^5 + 11*x^6 + 13*x^7 + 15*x^8 + 17*x^9 + ...


MATHEMATICA



PROG

(Magma) [2*nFloor((n+2) mod (n+1)): n in [0..70]]; // Vincenzo Librandi, Sep 21 2011
(Sage) def a(n) : return( dimension_cusp_forms( Gamma0(6), 2*n+2) ); # Michael Somos, Jul 03 2014
(GAP) Concatenation([0], List([1, 3..141])); # Muniru A Asiru, Jul 28 2018


CROSSREFS

Cf. A110185, continued fraction expansion of 2*tanh(1/2), and A204877, continued fraction expansion of 3*tanh(1/3). [Bruno Berselli, Jan 26 2012]


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



