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A239057 Sum of the parts in the partitions of 4n into 4 parts with smallest part equal to 1 minus the number of these partitions. 8
3, 28, 110, 285, 570, 1012, 1647, 2480, 3570, 4953, 6622, 8648, 11067, 13860, 17110, 20853, 25058, 29820, 35175, 41080, 47642, 54897, 62790, 71440, 80883, 91052, 102078, 113997, 126730, 140420, 155103, 170688, 187330, 205065, 223790, 243672, 264747, 286900 (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

FORMULA

a(n) = A239056(n) - A238705(n).

G.f.: x*(2*x^2+x+3)*(5*x^4+19*x^3+16*x^2+7*x+1)/((x^2+x+1)^2*(x-1)^4). - Alois P. Heinz, Mar 11 2014

EXAMPLE

For a(n) add the numbers in the first 3 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

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

     3               28            110             285        ..   a(n)

MATHEMATICA

b[n_] := (4 n - 1) 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}]/(4 n); Table[b[n], {n, 50}]

CoefficientList[Series[(2 x^2 + x + 3) (5 x^4 + 19 x^3 + 16 x^2 + 7 x + 1)/((x^2 + x + 1)^2 (x - 1)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 13 2014 *)

CROSSREFS

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

Sequence in context: A186429 A165393 A107651 * A100019 A053132 A316390

Adjacent sequences:  A239054 A239055 A239056 * A239058 A239059 A239060

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Mar 09 2014

STATUS

approved

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Last modified April 5 23:07 EDT 2020. Contains 333260 sequences. (Running on oeis4.)