A035371 Number of partitions of n into parts 5k+1 or 5k+2.
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, 134, 155, 175, 203, 230, 265, 298, 340, 383, 437, 492, 558, 624, 705, 789, 890, 993, 1115, 1241, 1391, 1548, 1730, 1919, 2139, 2370, 2638, 2919, 3239, 3576, 3962, 4372, 4836
Offset: 0
Keywords
Examples
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 + ...
Programs
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Mathematica
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 *) -
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 */
Formula
Euler transform of period 5 sequence [ 1, 1, 0, 0, 0, ...]. - Michael Somos, Feb 09 2012
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