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A239186 Sum of the largest two parts in the partitions of 4n into 4 parts with smallest part equal to 1. 4
2, 23, 93, 243, 492, 878, 1432, 2165, 3123, 4337, 5810, 7596, 9726, 12195, 15065, 18367, 22088, 26298, 31028, 36257, 42063, 48477, 55470, 63128, 71482, 80495, 90261, 100811, 112100, 124230, 137232, 151053, 165803, 181513, 198122, 215748, 234422, 254075 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.: x*(10*x^6+39*x^5+61*x^4+76*x^3+49*x^2+19*x+2) / ((x-1)^4*(x^2+x+1)^2). - Colin Barker, Mar 12 2014

EXAMPLE

For a(n) add the numbers in the first two 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 + 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

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

     2               23             93             243        ..   a(n)

MATHEMATICA

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

PROG

(PARI) Vec(x*(10*x^6+39*x^5+61*x^4+76*x^3+49*x^2+19*x+2)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Sep 22 2014

CROSSREFS

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

Sequence in context: A131464 A245331 A270868 * A238185 A053999 A131176

Adjacent sequences:  A239183 A239184 A239185 * A239187 A239188 A239189

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Mar 11 2014

STATUS

approved

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Last modified April 25 22:44 EDT 2019. Contains 322463 sequences. (Running on oeis4.)