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 A309793 Number of odd parts appearing among the second largest parts of the partitions of n into 4 parts. 2
 0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 5, 6, 8, 9, 11, 13, 17, 20, 24, 27, 32, 36, 42, 47, 54, 60, 68, 75, 85, 93, 103, 112, 124, 135, 149, 161, 176, 189, 205, 220, 239, 256, 276, 294, 316, 336, 360, 382, 408, 432, 460, 486, 517, 545, 577, 607, 642, 675, 713, 748 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,1,-2,2,-2,1,0,0,0,-1,2,-1). FORMULA a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (i mod 2). From Colin Barker, Aug 18 2019: (Start) G.f.: x^4*(1 - x + x^4) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x^4)). a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + 2*a(n-8) - 2*a(n-9) + a(n-10) - a(n-14) + 2*a(n-15) - a(n-16) for n>15. (End) [Recurrence verified by Wesley Ivan Hurt, Aug 24 2019] EXAMPLE Figure 1: The partitions of n into 4 parts for n = 8, 9, ..                                                          1+1+1+9                                                          1+1+2+8                                                          1+1+3+7                                                          1+1+4+6                                              1+1+1+8     1+1+5+5                                              1+1+2+7     1+2+2+7                                  1+1+1+7     1+1+3+6     1+2+3+6                                  1+1+2+6     1+1+4+5     1+2+4+5                                  1+1+3+5     1+2+2+6     1+3+3+5                      1+1+1+6     1+1+4+4     1+2+3+5     1+3+4+4          1+1+1+5     1+1+2+5     1+2+2+5     1+2+4+4     2+2+2+6          1+1+2+4     1+1+3+4     1+2+3+4     1+3+3+4     2+2+3+5          1+1+3+3     1+2+2+4     1+3+3+3     2+2+2+5     2+2+4+4          1+2+2+3     1+2+3+3     2+2+2+4     2+2+3+4     2+3+3+4          2+2+2+2     2+2+2+3     2+2+3+3     2+3+3+3     3+3+3+3 --------------------------------------------------------------------------   n  |      8           9          10          11          12        ... -------------------------------------------------------------------------- a(n) |      2           3           5           6           8        ... -------------------------------------------------------------------------- MATHEMATICA LinearRecurrence[{2, -1, 0, 0, 0, 1, -2, 2, -2, 1, 0, 0, 0, -1, 2, -1}, {0, 0, 0, 0, 1, 1, 1, 1, 2, 3, 5, 6, 8, 9, 11, 13}, 50] PROG (PARI) concat([0, 0, 0, 0], Vec(x^4*(1 - x + x^4) / ((1 - x)^4*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x^4)) + O(x^50))) \\ Colin Barker, Oct 10 2019 CROSSREFS Cf. A309795, A309797, A026928. Sequence in context: A191877 A277124 A094820 * A093689 A097702 A082583 Adjacent sequences:  A309790 A309791 A309792 * A309794 A309795 A309796 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Aug 17 2019 STATUS approved

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Last modified July 24 05:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)