A204472 Number of 8-element subsets that can be chosen from {1,2,...,8*n} having element sum 32*n+4.

0, 1, 526, 17575, 178870, 1016737, 4083008, 13011585, 35154340, 83916031, 181913856, 365087337, 687884214, 1229647953, 2102332580, 3459670513, 5507918992, 8518310823, 12841335118, 18922973607, 27323018256, 38735595881, 54012025302, 74186132807, 100502151596

Offset: 0

Author

Alois P. Heinz, Jan 16 2012

Keywords

• nonn
• easy

Comments

a(n) is the number of partitions of 32*n+4 into 8 distinct parts <= 8*n.

Examples

			a(2) = 526 because there are 526 8-element subsets that can be chosen from {1,2,...,16} having element sum 68: {1,2,3,4,13,14,15,16}, {1,2,3,5,12,14,15,16}, ..., {4,6,7,8,9,10,11,13}, {5,6,7,8,9,10,11,12}.
		

Links

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

Crossrefs

Column k=8 of A204459.

Programs

Maple

a:= n-> (Matrix(22, (i, j)-> `if`(i=j-1, 1, `if`(i=22, [-1, 4, -6, 6, -9, 13, -13, 13, -16, 19, -19, 18, -19, 19, -16, 13, -13, 13, -9, 6, -6, 4][j], 0)))^n. <<0, 1, 526, 17575, 178870, 1016737, 4083008, 13011585, 35154340, 83916031, 181913856, 365087337, 687884214, 1229647953, 2102332580, 3459670513, 5507918992, 8518310823, 12841335118, 18922973607, 27323018256, 38735595881>>)[1, 1]: seq(a(n), n=0..50);

Formula

G.f.: x*(289*x^20 +11190*x^19 +91493*x^18 +352388*x^17 +898356*x^16 +1737191*x^15 +2761013*x^14 +3796426*x^13 +4655081*x^12 +5159765*x^11 +5190716*x^10 +4740985*x^9 +3917109*x^8 +2893806*x^7 +1858105*x^6 +988551*x^5 +403560*x^4 +111720*x^3 +15477*x^2 +522*x+1) / ((x^4+x^3+x^2+x+1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^2+x+1)^2*(x-1)^8).