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 A309683 Number of odd parts appearing among the smallest parts of the partitions of n into 3 parts. 11
 0, 0, 0, 1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 9, 9, 12, 12, 15, 15, 18, 18, 22, 22, 26, 26, 30, 30, 35, 35, 40, 40, 45, 45, 51, 51, 57, 57, 63, 63, 70, 70, 77, 77, 84, 84, 92, 92, 100, 100, 108, 108, 117, 117, 126, 126, 135, 135, 145, 145, 155, 155, 165, 165, 176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,1,-1,-1,1). FORMULA a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (j mod 2). From Colin Barker, Aug 22 2019: (Start) G.f.: x^3 / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)*(1 + x + x^2)). a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-6) - a(n-7) - a(n-8) + a(n-9) for n>8. (End) EXAMPLE Figure 1: The partitions of n into 3 parts for n = 3, 4, ...                                                           1+1+8                                                    1+1+7  1+2+7                                                    1+2+6  1+3+6                                             1+1+6  1+3+5  1+4+5                                      1+1+5  1+2+5  1+4+4  2+2+6                               1+1+4  1+2+4  1+3+4  2+2+5  2+3+5                        1+1+3  1+2+3  1+3+3  2+2+4  2+3+4  2+4+4          1+1+1  1+1+2  1+2+2  2+2+2  2+2+3  2+3+3  3+3+3  3+3+4    ... -----------------------------------------------------------------------   n  |     3      4      5      6      7      8      9     10      ... ----------------------------------------------------------------------- a(n) |     1      1      2      2      3      3      5      5      ... ----------------------------------------------------------------------- MATHEMATICA Table[Sum[Sum[Mod[j, 2], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 80}] LinearRecurrence[{1, 1, -1, 0, 0, 1, -1, -1, 1}, {0, 0, 0, 1, 1, 2, 2, 3, 3}, 50] (* Wesley Ivan Hurt, Aug 28 2019 *) CROSSREFS Cf. A026923, A026927, A309684, A309685, A309686, A309687, A309688, A309689, A309690, A309692, A309694. Sequence in context: A121261 A085885 A309685 * A283529 A064986 A029019 Adjacent sequences:  A309680 A309681 A309682 * A309684 A309685 A309686 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Aug 12 2019 STATUS approved

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Last modified December 11 18:34 EST 2019. Contains 329925 sequences. (Running on oeis4.)