A204470 Number of 6-element subsets that can be chosen from {1,2,...,6*n} having element sum 18*n+3.

0, 1, 58, 676, 3486, 11963, 32134, 73294, 148718, 276373, 479632, 787986, 1237756, 1872809, 2745266, 3916220, 5456444, 7447107, 9980486, 13160678, 17104314, 21941271, 27815384, 34885162, 43324496, 53323377, 65088604, 78844500, 94833624, 113317483, 134577246

Offset: 0

Author

Alois P. Heinz, Jan 16 2012

Keywords

• nonn
• easy

Comments

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

Examples

			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}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=6 of A204459.

Programs

Maple

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);

Formula

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).