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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239056 Sum of the parts in the partitions of 4n into 4 parts with smallest part = 1. 9
4, 32, 120, 304, 600, 1056, 1708, 2560, 3672, 5080, 6776, 8832, 11284, 14112, 17400, 21184, 25432, 30240, 35644, 41600, 48216, 55528, 63480, 72192, 81700, 91936, 103032, 115024, 127832, 141600, 156364, 172032, 188760, 206584, 225400, 245376, 266548, 288800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms are multiples of 4.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for sequences related to partitions

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

FORMULA

G.f.: 4*x*(2*x^6+10*x^5+16*x^4+22*x^3+15*x^2+6*x+1) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Mar 10 2014

EXAMPLE

For a(n) add the parts in the partitions of 4n with smallest part = 1.

                                              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 + 1 + 1 + 1    9 + 4 + 2 + 1

                              8 + 2 + 1 + 1    8 + 5 + 2 + 1

                              7 + 3 + 1 + 1    7 + 6 + 2 + 1

                              6 + 4 + 1 + 1    9 + 3 + 3 + 1

                              5 + 5 + 1 + 1    8 + 4 + 3 + 1

                              7 + 2 + 2 + 1    7 + 5 + 3 + 1

               5 + 1 + 1 + 1  6 + 3 + 2 + 1    6 + 6 + 3 + 1

               4 + 2 + 1 + 1  5 + 4 + 2 + 1    7 + 4 + 4 + 1

               3 + 3 + 1 + 1  5 + 3 + 3 + 1    6 + 5 + 4 + 1

1 + 1 + 1 + 1  3 + 2 + 2 + 1  4 + 4 + 3 + 1    5 + 5 + 5 + 1

    4(1)            4(2)           4(3)            4(4)       ..   4n

------------------------------------------------------------------------

     4               32            120             304        ..   a(n)

MATHEMATICA

b[n_] := Sum[((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i) + (i + 2) (Floor[(4 n - 2 - i)/2] - i)) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[b[n], {n, 50}]

LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {4, 32, 120, 304, 600, 1056, 1708, 2560}, 40] (* Harvey P. Dale, Oct 18 2018 *)

PROG

Vec(4*x*(2*x^6+10*x^5+16*x^4+22*x^3+15*x^2+6*x+1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Sep 22 2014

CROSSREFS

Cf. A238328, A238340, A238702, A238705, A238706.

Sequence in context: A211627 A033430 A267668 * A088658 A088802 A123854

Adjacent sequences:  A239053 A239054 A239055 * A239057 A239058 A239059

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Mar 09 2014

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 7 13:32 EDT 2020. Contains 333305 sequences. (Running on oeis4.)