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 A239667 Sum of the largest parts of the partitions of 4n into 4 parts. 2
 1, 17, 84, 262, 629, 1289, 2370, 4014, 6393, 9703, 14150, 19974, 27439, 36815, 48410, 62556, 79587, 99879, 123832, 151844, 184359, 221845, 264764, 313628, 368973, 431325, 501264, 579394, 666305, 762645, 869086, 986282, 1114949, 1255827, 1409634, 1577154, 1759195, 1956539, 2170038, 2400568 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS A. Osorio, A Sequential Allocation Problem: The Asymptotic Distribution of Resources, Munich Personal RePEc Archive, 2014. Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,6,-3,3,-3,1). FORMULA G.f.: -x*(9*x^6+32*x^5+50*x^4+58*x^3+36*x^2+14*x+1) / ((x-1)^5*(x^2+x+1)^2). - Colin Barker, Mar 23 2014 Let b(1) = 4, with b(n) = (n/(n-1)) * b(n-1) + 4n * Sum_{i=0..2n} (floor((4n-2-i)/2)-i) * floor((sign(floor((4n-2-i)/2)-i)+2)/2). Then a(1) = 1, with  a(n) = a(n-1) + b(n-1)/(4n-4) + Sum_{i=j+1..floor((4n-2-j)/2)} ( Sum_{j=0..2n} (4n-2-i-j) * floor((sign(floor((4n-2-j)/2)-j)+2)/2) ). - Wesley Ivan Hurt, Jun 13 2014 EXAMPLE Add the numbers in the first column for a(n):                                              13 + 1 + 1 + 1                                              12 + 2 + 1 + 1                                              11 + 3 + 1 + 1                                              10 + 4 + 1 + 1                                               9 + 5 + 1 + 1                                               8 + 6 + 1 + 1                                               7 + 7 + 1 + 1                                              11 + 2 + 2 + 1                                              10 + 3 + 2 + 1                                               9 + 4 + 2 + 1                                               8 + 5 + 2 + 1                                               7 + 6 + 2 + 1                                               9 + 3 + 3 + 1                                               8 + 4 + 3 + 1                                               7 + 5 + 3 + 1                                               6 + 6 + 3 + 1                                               7 + 4 + 4 + 1                                               6 + 5 + 4 + 1                                               5 + 5 + 5 + 1                               9 + 1 + 1 + 1  10 + 2 + 2 + 2                               8 + 2 + 1 + 1   9 + 3 + 2 + 2                               7 + 3 + 1 + 1   8 + 4 + 2 + 2                               6 + 4 + 1 + 1   7 + 5 + 2 + 2                               5 + 5 + 1 + 1   6 + 6 + 2 + 2                               7 + 2 + 2 + 1   8 + 3 + 3 + 2                               6 + 3 + 2 + 1   7 + 4 + 3 + 2                               5 + 4 + 2 + 1   6 + 5 + 3 + 2                               5 + 3 + 3 + 1   6 + 4 + 4 + 2                               4 + 4 + 3 + 1   5 + 5 + 4 + 2                5 + 1 + 1 + 1  6 + 2 + 2 + 2   7 + 3 + 3 + 3                4 + 2 + 1 + 1  5 + 3 + 2 + 2   6 + 4 + 3 + 3                3 + 3 + 1 + 1  4 + 4 + 2 + 2   5 + 5 + 3 + 3                3 + 2 + 2 + 1  4 + 3 + 3 + 2   5 + 4 + 4 + 3 1 + 1 + 1 + 1  2 + 2 + 2 + 2  3 + 3 + 3 + 3   4 + 4 + 4 + 4     4(1)            4(2)           4(3)            4(4)       ..   4n ------------------------------------------------------------------------      1               17             84             262        ..   a(n) MATHEMATICA CoefficientList[Series[-(9*x^6 + 32*x^5 + 50*x^4 + 58*x^3 + 36*x^2 + 14*x + 1)/((x - 1)^5*(x^2 + x + 1)^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jun 13 2014 *) LinearRecurrence[{3, -3, 3, -6, 6, -3, 3, -3, 1}, {1, 17, 84, 262, 629, 1289, 2370, 4014, 6393}, 50](* Vincenzo Librandi, Aug 29 2015 *) PROG (PARI) Vec(-x*(9*x^6+32*x^5+50*x^4+58*x^3+36*x^2+14*x+1) / ((x-1)^5*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Mar 23 2014 (MAGMA) I:=[1, 17, 84, 262, 629, 1289, 2370, 4014, 6393]; [n le 9 select I[n] else 3*Self(n-1)-3*Self(n-2)+3*Self(n-3)-6*Self(n-4)+6*Self(n-5)-3*Self(n-6)+3*Self(n-7)-3*Self(n-8)+Self(n-9): n in [1..45]]; // Vincenzo Librandi, Aug 29 2015 CROSSREFS Cf. A238328, A238340, A238702, A238705, A238706, A239056, A239057, A239059, A239186. Sequence in context: A158528 A197346 A213436 * A156968 A212487 A288420 Adjacent sequences:  A239664 A239665 A239666 * A239668 A239669 A239670 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt and Antonio Osorio, Mar 23 2014 STATUS approved

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Last modified June 16 21:13 EDT 2019. Contains 324155 sequences. (Running on oeis4.)