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

 

Logo

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!)
A241084 Sum of the second largest parts of the partitions of 4n into 4 parts. 2
1, 10, 46, 141, 334, 680, 1247, 2106, 3348, 5077, 7396, 10432, 14325, 19210, 25250, 32621, 41490, 52056, 64531, 79114, 96040, 115557, 137896, 163328, 192137, 224586, 260982, 301645, 346870, 397000, 452391, 513370, 580316, 653621, 733644, 820800, 915517, 1018186, 1129258, 1249197 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..40.

A. Osorio, A Sequential Allocation Problem: The Asymptotic Distribution of Resources, Munich Personal RePEc Archive, 2014.

Index entries for sequences related to partitions

Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,6,-3,3,-3,1).

FORMULA

G.f.: -x*(5*x^6+17*x^5+25*x^4+30*x^3+19*x^2+7*x+1) / ((x-1)^5*(x^2+x+1)^2). - Colin Barker, Apr 16 2014

Recurrence: Let b(1) = 4, with b(n) = (n/(n-1)) * b(n-1) + 4n*Sum_{i=0..2n} (floor((4n-2-i)/2)-i) * (floor((sign((floor((4n-2-i)/2)-i))+2)/2)) for n>1. Then a(1) = 1, with a(n) = a(n-1) + b(n-1)/(4n-4) + Sum_{j=0..2n} (Sum_{i=j+1..floor((4n-2-j)/2)} i * (floor((sign((floor((4n-2-j)/2)-j))+ 2)/2)) ), for n>1. - Wesley Ivan Hurt, Jun 27 2014

EXAMPLE

For a(n) add the numbers in the second columns.

                                             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

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

     1               10             46             141        ..   a(n)

MATHEMATICA

CoefficientList[Series[-(5*x^6 + 17*x^5 + 25*x^4 + 30*x^3 + 19*x^2 + 7*x + 1)/((x - 1)^5*(x^2 + x + 1)^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jun 13 2014 *)

LinearRecurrence[{3, -3, 3, -6, 6, -3, 3, -3, 1}, {1, 10, 46, 141, 334, 680, 1247, 2106, 3348}, 50] (* Vincenzo Librandi, Aug 29 2015 *)

PROG

(PARI) Vec(-x*(5*x^6+17*x^5+25*x^4+30*x^3+19*x^2+7*x+1)/((x-1)^5*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Apr 16 2014

(MAGMA) I:=[1, 10, 46, 141, 334, 680, 1247, 2106, 3348]; [n le 9 select I[n] else 3*Self(n-1)-3*Self(n-2)+3*Self(n-3)-6*Self(n-4)+6*Self(n-5)-3*Self(n-6)+3*Self(n-7)-3*Self(n-8)+Self(n-9): n in [1..45]]; // Vincenzo Librandi, Aug 29 2015

CROSSREFS

Cf. A238328, A238340, A238702, A238705, A238706, A239056, A239057, A239059.

Sequence in context: A244246 A288117 A213834 * A106600 A085437 A024166

Adjacent sequences:  A241081 A241082 A241083 * A241085 A241086 A241087

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt and Antonio Osorio, Apr 15 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 December 4 06:41 EST 2021. Contains 349476 sequences. (Running on oeis4.)