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 A238706 Sum of the smallest parts of the partitions of 4n into 4 parts with smallest part greater than 1. 10
 0, 2, 11, 36, 89, 183, 335, 565, 894, 1347, 1952, 2738, 3738, 4988, 6525, 8390, 10627, 13281, 16401, 20039, 24248, 29085, 34610, 40884, 47972, 55942, 64863, 74808, 85853, 98075, 111555, 126377, 142626, 160391, 179764, 200838, 223710, 248480, 275249, 304122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 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^2*(x-2)*(x+1)*(2*x^2+x+1) / ((x-1)^5*(x^2+x+1)). - Colin Barker, Mar 23 2014 a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 5*a(n-4) + 6*a(n-5) - 4*a(n-6) + a(n-7) for n > 7. - Wesley Ivan Hurt, Oct 07 2017 EXAMPLE Add the numbers > 1 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 ------------------------------------------------------------------------      0               2              11              36        ..   a(n) MATHEMATICA a[1] = 4; a[n_] := (n/(n - 1))*a[n - 1] + 4 n*Sum[(Floor[(4 n - 2 - i)/2] - i)*(Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; b[n_] := a[n]/(4 n); b[0] = 0; c[1] = 1; c[n_] := b[n] + c[n - 1]; Table[c[n] - (b[n] - b[n - 1]), {n, 50}] CoefficientList[Series[x (x - 2) (x + 1) (2 x^2 + x + 1)/((x - 1)^5 (x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 24 2014 *) PROG (PARI) concat(0, Vec(x^2*(x-2)*(x+1)*(2*x^2+x+1)/((x-1)^5*(x^2+x+1)) + O(x^100))) \\ Colin Barker, Mar 23 2014 (MAGMA) I:=[0, 2, 11, 36, 89, 183, 335]; [n le 7 select I[n] else 4*Self(n-1)-6*Self(n-2)+5*Self(n-3)-5*Self(n-4)+6*Self(n-5)-4*Self(n-6)+Self(n-7): n in [1..40]]; // Vincenzo Librandi, Mar 24 2014 CROSSREFS Cf. A238328, A238340, A238702, A238705. Sequence in context: A154416 A184538 A316322 * A071244 A005583 A176916 Adjacent sequences:  A238703 A238704 A238705 * A238707 A238708 A238709 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt and Antonio Osorio, Mar 03 2014 STATUS approved

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)