

A051275


Expansion of (1+x^2)/((1x^2)*(1x^3)).


2



1, 0, 2, 1, 2, 2, 3, 2, 4, 3, 4, 4, 5, 4, 6, 5, 6, 6, 7, 6, 8, 7, 8, 8, 9, 8, 10, 9, 10, 10, 11, 10, 12, 11, 12, 12, 13, 12, 14, 13, 14, 14, 15, 14, 16, 15, 16, 16, 17, 16, 18, 17, 18, 18, 19, 18, 20, 19, 20, 20, 21, 20, 22, 21, 22, 22, 23, 22, 24, 23, 24, 24
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OFFSET

0,3


COMMENTS

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 12 ).
Diagonal sums of A117567.  Paul Barry, Mar 29 2006
First differences of A156040.  Bob Selcoe, Feb 07 2014
Also first difference of diagonal sums of the triangle formed by rows T(2,k) k=0,1...,2m of ascending mnomial triangles (see A004737).  Bob Selcoe, Feb 07 2014


LINKS

Table of n, a(n) for n=0..71.
Luke James and Ben Salisbury, The weight function for monomial crystals of affine type, arXiv:1707.03159 [math.CO], 2017, p. 20 (sequence b_k).
William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))
William A. Stein, The modular forms database
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,1).


FORMULA

From Paul Barry, Mar 29 2006: (Start)
a(n) = a(n2) + a(n3)  a(n5);
a(n) = cos(2*Pi*n/3 + Pi/3)/3  sqrt(3)*sin(2*Pi*n/3 + Pi/3)/9 + (1)^n/2 + (2n+3)/6;
a(n) = Sum_{k=0..floor(n/2)} F(L((n2k+2)/3)) where L(j/p) is the Legendre symbol of j and p. (End)
a(n) = 2*floor(n/2) + floor((n+4)/3)  n.  Ridouane Oudra, Nov 26 2019


PROG

(PARI) Vec((1+x^2)/((1x^2)*(1x^3))+ O(x^80)) \\ Michel Marcus, Nov 26 2019


CROSSREFS

Cf. A051274, A117567, A156040.
Sequence in context: A172245 A238781 A319439 * A025799 A282537 A053267
Adjacent sequences: A051272 A051273 A051274 * A051276 A051277 A051278


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



