The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309684 Sum of the odd parts appearing among the smallest parts of the partitions of n into 3 parts. 12
 0, 0, 0, 1, 1, 2, 2, 3, 3, 7, 7, 11, 11, 15, 15, 24, 24, 33, 33, 42, 42, 58, 58, 74, 74, 90, 90, 115, 115, 140, 140, 165, 165, 201, 201, 237, 237, 273, 273, 322, 322, 371, 371, 420, 420, 484, 484, 548, 548, 612, 612, 693, 693, 774, 774, 855, 855, 955, 955 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Jinyuan Wang, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,2,-2,-2,2,0,0,-1,1,1,-1). FORMULA a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} j * (j mod 2). From Colin Barker, Aug 22 2019: (Start) G.f.: x^3*(1 + x^2)*(1 - x^2 + x^4) / ((1 - x)^4*(1 + x)^3*(1 - x + x^2)^2*(1 + x + x^2)^2). a(n) = a(n-1) + a(n-2) - a(n-3) + 2*a(n-6) - 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - a(n-12) + a(n-13) + a(n-14) - a(n-15) for n > 14. (End) a(n) = (-4*s^3+(2*t-7)*s^2+(4*t-1)*s+2*t+2)/2, where s = floor((n-3)/6) and t = floor((n-3)/2). - Wesley Ivan Hurt, Oct 27 2021 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      7      7      ... ----------------------------------------------------------------------- MATHEMATICA Table[Sum[Sum[j*Mod[j, 2], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 0, 80}] LinearRecurrence[{1, 1, -1, 0, 0, 2, -2, -2, 2, 0, 0, -1, 1, 1, -1}, {0, 0, 0, 1, 1, 2, 2, 3, 3, 7, 7, 11, 11, 15, 15}, 20] (* Wesley Ivan Hurt, Aug 29 2019 *) PROG (PARI) a(n) = sum(j = 1, floor(n/3), sum(i = j, floor((n-j)/2), j * (j%2))); \\ Jinyuan Wang, Aug 29 2019 CROSSREFS Cf. A026923, A026927, A309683, A309685, A309686, A309687, A309688, A309689, A309690, A309692, A309694. Sequence in context: A295510 A324520 A307737 * A330950 A032060 A241385 Adjacent sequences:  A309681 A309682 A309683 * A309685 A309686 A309687 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Aug 12 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 12:16 EST 2021. Contains 349462 sequences. (Running on oeis4.)