%I #12 Aug 27 2015 05:56:32

%S 1,1,2,2,3,3,5,6,8,9,11,13,17,20,25,28,34,39,48,55,65,74,87,100,118,

%T 134,155,175,203,230,265,298,340,383,437,492,558,624,705,789,890,993,

%U 1115,1241,1391,1548,1730,1919,2139,2370,2638,2919,3239,3576,3962,4372,4836

%N Number of partitions of n into parts 5k+1 or 5k+2.

%F Euler transform of period 5 sequence [ 1, 1, 0, 0, 0, ...]. - _Michael Somos_, Feb 09 2012

%F a(n) ~ exp(2*Pi*sqrt(n/15)) * Gamma(1/5) * Gamma(2/5) / (4 * 3^(1/20) * 5^(9/20) * Pi^(7/5) * n^(11/20)). - _Vaclav Kotesovec_, Aug 27 2015

%e 1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + 8*x^8 + 9*x^9 + ...

%t nmax = 100; CoefficientList[Series[Product[1/((1 - x^(5k+1))*(1 - x^(5k+2))), {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)\5, (1 - x^(5*k - 4)) * (1 - x^(5*k - 3)), 1 + x * O(x^n)), n))} /* _Michael Somos_, Feb 09 2012 */

%K nonn

%O 0,3

%A _Olivier Gérard_