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 A238702 Sum of the smallest parts of the partitions of 4n into 4 parts. 16
 1, 6, 21, 55, 119, 227, 396, 645, 996, 1474, 2106, 2922, 3955, 5240, 6815, 8721, 11001, 13701, 16870, 20559, 24822, 29716, 35300, 41636, 48789, 56826, 65817, 75835, 86955, 99255, 112816, 127721, 144056, 161910, 181374, 202542, 225511, 250380, 277251, 306229 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Partial sums of A238340. - Wesley Ivan Hurt, May 27 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..100 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 (4,-6,5,-5,6,-4,1). FORMULA G.f.: -x*(x+1)*(2*x^2+x+1) / ((x-1)^5*(x^2+x+1)). - Colin Barker, Mar 10 2014 a(n) = (1/9)*n^4 + (1/3)*n^3 + (5/18)*n^2 + (1/6)*n + O(1). - Ralf Stephan, May 29 2014 a(n) = Sum_{i=1..n} A238340(i). - Wesley Ivan Hurt, May 29 2014 a(n) = (1/4) * Sum_{i=1..n} A238328(i)/i. - Wesley Ivan Hurt, May 29 2014 Recurrence: 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) = b(n)/(4n) + a(n-1), for n>1. - Wesley Ivan Hurt, Jun 27 2014 EXAMPLE Add the numbers in the last 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               6              21              55        ..   a(n) MATHEMATICA CoefficientList[Series[(x + 1)*(2*x^2 + x + 1)/((1 - x)^5*(x^2 + x + 1)), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jun 27 2014 *) LinearRecurrence[{4, -6, 5, -5, 6, -4, 1}, {1, 6, 21, 55, 119, 227, 396}, 50] (* Vincenzo Librandi, Aug 29 2015 *) PROG (PARI) Vec(-x*(x+1)*(2*x^2+x+1)/((x-1)^5*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Mar 23 2014 CROSSREFS Cf. A238328, A238340. Sequence in context: A115052 A025203 A262719 * A162539 A259474 A002817 Adjacent sequences:  A238699 A238700 A238701 * A238703 A238704 A238705 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt and Antonio Osorio, Mar 03 2014 STATUS approved

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)