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 A035384 Number of partitions of n into parts 6k+2 or 6k+3. 0

%I #12 Aug 27 2015 06:04:35

%S 1,0,1,1,1,1,2,1,3,3,3,4,5,4,7,7,8,10,12,11,16,16,18,22,25,25,33,34,

%T 38,45,50,52,65,67,75,87,95,101,121,126,141,160,174,187,218,229,254,

%U 285,308,333,380,401,443,492,530,574,646,683,752,828,890,964,1072,1137,1246

%N Number of partitions of n into parts 6k+2 or 6k+3.

%F Euler transform of period 6 sequence [ 0, 1, 1, 0, 0, 0, ...]. - _Michael Somos_, Feb 09 2012

%F G.f.: 1 / (Product_{k>0} (1 - x^(6*k - 4)) * (1 - x^(6*k - 3))). - _Michael Somos_, Feb 09 2012

%F a(n) ~ exp(Pi*sqrt(2*n)/3) * Gamma(1/3) / (4 * 2^(1/3) * sqrt(3) * Pi^(2/3) * n^(2/3)). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 100; CoefficientList[Series[Product[1/((1 - x^(6k+2))*(1 - x^(6k+3))), {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%o (PARI) {a(n) = if( n<0, 0, polcoeff( 1 / prod( k=1, (n+4)\6, (1 - x^(6*k - 4)) * (1 - x^(6*k - 3)), 1 + x * O(x^n)), n))} /* _Michael Somos_, Feb 09 2012 */

%K nonn

%O 0,7