OFFSET
0,6
COMMENTS
a(k) for k>0 is the dimension of the space of Siegel modular forms of genus 2 and weight 2k (for the full modular group Gamma_2). Also: Number of solutions of 4x+6y+10z+12w=k in nonnegative integers x,y,z,w. - Kilian Kilger (kilian(AT)nihilnovi.de), Sep 26 2009
Number of partitions of n into parts 2, 3, 5, and 6. - Joerg Arndt, Jun 21 2014
REFERENCES
H. Klingen, Intro. lectures on Siegel modular forms, Cambridge, p. 123, Corollary.
L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 31).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)
W. C. Huffman, The biweight enumerator of self-orthogonal binary codes, Discr. Math. Vol. 26 1979, pp. 129-143.
J. Igusa, On Siegel modular forms of genus 2, Amer. J. Math., 84 (1962), 175-200.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,1,-1,-2,-1,1,0,0,1,1,0,-1).
FORMULA
a(n) ~ 1/1080*n^3. - Ralf Stephan, Apr 29 2014
a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=1, a(5)=2, a(6)=3, a(7)=2, a(8)=4, a(9)=4, a(10)=5, a(11)=6, a(12)=8, a(13)=7, a(14)=10, a(15)=11, a(n)= a(n-2)+ a(n-3)+a(n-6)-a(n-7)- 2*a(n-8)-a(n-9)+a(n-10)+a(n-13)+ a(n-14)- a(n-16). - Harvey P. Dale, May 12 2015
MAPLE
M := Matrix(16, (i, j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 6, 10, 13, 14])) then 1 elif j=1 and member(i, [7, 9, 16]) then -1 elif j=1 and i=8 then -2 else 0 fi): a:= n -> (M^(n))[1, 1]: seq(a(n), n=0..54); # Alois P. Heinz, Jul 25 2008
MATHEMATICA
CoefficientList[Series[1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^6)), {x, 0, 54}], x] (* Jean-François Alcover, Mar 20 2011 *)
LinearRecurrence[{0, 1, 1, 0, 0, 1, -1, -2, -1, 1, 0, 0, 1, 1, 0, -1}, {1, 0, 1, 1, 1, 2, 3, 2, 4, 4, 5, 6, 8, 7, 10, 11}, 60] (* Harvey P. Dale, May 12 2015 *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Definition corrected by Kilian Kilger (kilian(AT)nihilnovi.de), Sep 25 2009
STATUS
approved