A204470 - OEIS

%I #12 Oct 31 2018 17:03:38

%S 0,1,58,676,3486,11963,32134,73294,148718,276373,479632,787986,

%T 1237756,1872809,2745266,3916220,5456444,7447107,9980486,13160678,

%U 17104314,21941271,27815384,34885162,43324496,53323377,65088604,78844500,94833624,113317483,134577246

%N Number of 6-element subsets that can be chosen from {1,2,...,6*n} having element sum 18*n+3.

%C a(n) is the number of partitions of 18*n+3 into 6 distinct parts <= 6*n.

%H Alois P. Heinz, <a href="/A204470/b204470.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: x*(32*x^9 +352*x^8 +979*x^7 +1370*x^6 +1425*x^5 +1394*x^4 +1072*x^3 +449*x^2 +54*x+1) / ((x+1)*(x^4+x^3+x^2+x+1)*(x-1)^6).

%e a(2) = 58 because there are 58 6-element subsets that can be chosen from {1,2,...,12} having element sum 39: {1,2,3,10,11,12}, {1,2,4,9,11,12}, ..., {3,5,6,7,8,10}, {4,5,6,7,8,9}.

%p a:= n-> (Matrix(11, (i, j)-> `if`(i=j-1, 1, `if`(i=11, [-1, 4, -5, 0, 5, -3, -3, 5, 0, -5, 4][j], 0)))^n. <<0, 1, 58, 676, 3486, 11963, 32134, 73294, 148718, 276373, 479632>>)[1, 1]: seq(a(n), n=0..50);

%Y Column k=6 of A204459.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Jan 16 2012