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 A256328 Number of partitions of 6n into exactly 4 parts. 3
 0, 2, 15, 47, 108, 206, 351, 551, 816, 1154, 1575, 2087, 2700, 3422, 4263, 5231, 6336, 7586, 8991, 10559, 12300, 14222, 16335, 18647, 21168, 23906, 26871, 30071, 33516, 37214, 41175, 45407, 49920, 54722, 59823, 65231, 70956, 77006, 83391, 90119, 97200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1). FORMULA a(n) = (-1+(-1)^n+6*n^2+12*n^3)/8. a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5) for n>4. G.f.: x*(x+2)*(x^2+4*x+1) / ((x-1)^4*(x+1)). EXAMPLE For n=1 the 2 partitions of 6*1 = 6 are [1,1,1,3] and [1,1,2,2]. MATHEMATICA LinearRecurrence[{3, -2, -2, 3, -1}, {0, 2, 15, 47, 108}, 50] (* Harvey P. Dale, Mar 22 2020 *) PROG (PARI) concat(0, vector(40, n, k=0; forpart(p=6*n, k++, , [4, 4]); k)) (PARI) concat(0, Vec(x*(x+2)*(x^2+4*x+1)/((x-1)^4*(x+1)) + O(x^100))) CROSSREFS Cf. A256327 (5n), A256329 (7n). Sequence in context: A229013 A323685 A336209 * A041719 A133777 A025213 Adjacent sequences:  A256325 A256326 A256327 * A256329 A256330 A256331 KEYWORD nonn,easy AUTHOR Colin Barker, Mar 25 2015 STATUS approved

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Last modified August 5 08:44 EDT 2021. Contains 346464 sequences. (Running on oeis4.)