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A081753 a(n) = floor(n/12) if n == 2 (mod 12); a(n) = floor(n/12) + 1 otherwise.

%I A081753 #28 May 31 2022 19:02:35
%S A081753 1,1,0,1,1,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,2,2,3,3,2,3,3,3,3,3,3,3,
%T A081753 3,3,4,4,3,4,4,4,4,4,4,4,4,4,5,5,4,5,5,5,5,5,5,5,5,5,6,6,5,6,6,6,6,6,
%U A081753 6,6,6,6,7,7,6,7,7,7,7,7,7,7,7,7,8,8,7,8,8,8,8,8,8,8,8,8,9,9,8,9,9,9,9,9,9
%N A081753 a(n) = floor(n/12) if n == 2 (mod 12); a(n) = floor(n/12) + 1 otherwise.
%C A081753 a(2n) = dimension of M(2n), where M(2n) denotes the complex vector space of modular forms of weight 2n for the group : PSL2(Z). dimension of M(2n+1) = 0.
%C A081753 See A103221(n) for the dimension of M(2n). The Apostol reference, p. 119, eq. (9) uses even k. - _Wolfdieter Lang_, Sep 16 2016
%C A081753 The space of modular forms is generated by E_4 (A004009) and E_6 (A013973) both of even weight. This is why the space of modular forms of odd weight is trivial. - _Michael Somos_, Dec 11 2018
%D A081753 Apostol, Tom M., Modular Functions and Dirichlet Series in Number Theory, second edition, Springer, 1990.
%D A081753 Yves Hellegouarch, "Invitation aux mathématiques de Fermat-Wiles", Dunod, 2ème édition, p. 285
%H A081753 Robert Israel, <a href="/A081753/b081753.txt">Table of n, a(n) for n = 0..10000</a>
%H A081753 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).
%F A081753 a(n) = floor(n/12) if n == 2 (mod 12); a(n) = floor(n/12) + 1 otherwise.
%F A081753 G.f.: (1-x^2+x^3)/(1-x-x^12+x^13). - _Robert Israel_, Sep 16 2016
%F A081753 a(2*n) = A008615(n+2), a(2*n+1) = A097992(n). - _Michael Somos_, Dec 11 2018
%e A081753 G.f. = 1 + x + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + 2*x^12 + ... - _Michael Somos_, Dec 11 2018
%p A081753 seq(floor(n/12)+1-charfcn[0](n-2 mod 12), n=0..100); # _Robert Israel_, Sep 16 2016
%t A081753 Table[If[Mod[n, 12] == 2, Floor[n/12], Floor[n/12] + 1], {n, 0, 120}] (* or *)
%t A081753 CoefficientList[Series[(1 - x^2 + x^3)/(1 - x - x^12 + x^13), {x, 0, 120}], x] (* _Michael De Vlieger_, Sep 19 2016 *)
%t A081753 a[ n_] := Quotient[n, 12] + Boole[Mod[n, 12] != 2]; (* _Michael Somos_, Dec 11 2018 *)
%o A081753 (PARI) a(k) = if(k%12-2, floor(k/12)+1, floor(k/12))
%o A081753 (PARI) {a(n) = n\12 + (n%12!=2)}; /* _Michael Somos_, Dec 11 2018 */
%Y A081753 Cf. A008615, A097992, A103221.
%K A081753 nonn,easy
%O A081753 0,13
%A A081753 _Benoit Cloitre_, Apr 08 2003