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 A239056 Sum of the parts in the partitions of 4n into 4 parts with smallest part = 1. 9
 4, 32, 120, 304, 600, 1056, 1708, 2560, 3672, 5080, 6776, 8832, 11284, 14112, 17400, 21184, 25432, 30240, 35644, 41600, 48216, 55528, 63480, 72192, 81700, 91936, 103032, 115024, 127832, 141600, 156364, 172032, 188760, 206584, 225400, 245376, 266548, 288800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms are multiples of 4. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1). FORMULA G.f.: 4*x*(2*x^6+10*x^5+16*x^4+22*x^3+15*x^2+6*x+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Mar 10 2014 EXAMPLE For a(n) add the parts in the partitions of 4n with smallest part = 1.                                               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 + 1 + 1 + 1    9 + 4 + 2 + 1                               8 + 2 + 1 + 1    8 + 5 + 2 + 1                               7 + 3 + 1 + 1    7 + 6 + 2 + 1                               6 + 4 + 1 + 1    9 + 3 + 3 + 1                               5 + 5 + 1 + 1    8 + 4 + 3 + 1                               7 + 2 + 2 + 1    7 + 5 + 3 + 1                5 + 1 + 1 + 1  6 + 3 + 2 + 1    6 + 6 + 3 + 1                4 + 2 + 1 + 1  5 + 4 + 2 + 1    7 + 4 + 4 + 1                3 + 3 + 1 + 1  5 + 3 + 3 + 1    6 + 5 + 4 + 1 1 + 1 + 1 + 1  3 + 2 + 2 + 1  4 + 4 + 3 + 1    5 + 5 + 5 + 1     4(1)            4(2)           4(3)            4(4)       ..   4n ------------------------------------------------------------------------      4               32            120             304        ..   a(n) MATHEMATICA b[n_] := Sum[((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i) + (i + 2) (Floor[(4 n - 2 - i)/2] - i)) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[b[n], {n, 50}] LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {4, 32, 120, 304, 600, 1056, 1708, 2560}, 40] (* Harvey P. Dale, Oct 18 2018 *) PROG Vec(4*x*(2*x^6+10*x^5+16*x^4+22*x^3+15*x^2+6*x+1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Sep 22 2014 CROSSREFS Cf. A238328, A238340, A238702, A238705, A238706. Sequence in context: A211627 A033430 A267668 * A088658 A088802 A123854 Adjacent sequences:  A239053 A239054 A239055 * A239057 A239058 A239059 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Mar 09 2014 STATUS approved

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Last modified April 7 13:32 EDT 2020. Contains 333305 sequences. (Running on oeis4.)