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 A204470 Number of 6-element subsets that can be chosen from {1,2,...,6*n} having element sum 18*n+3. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the number of partitions of 18*n+3 into 6 distinct parts <= 6*n. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 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). EXAMPLE 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}. 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); CROSSREFS Column k=6 of A204459. Sequence in context: A249468 A232378 A246894 * A254954 A172215 A305263 Adjacent sequences: A204467 A204468 A204469 * A204471 A204472 A204473 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Jan 16 2012 STATUS approved

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)