A256235 Sum of all the parts in the partitions of 5n into 5 parts.

0, 5, 70, 450, 1680, 4800, 11310, 23590, 44600, 78615, 130550, 207075, 315600, 465790, 667940, 935250, 1281520, 1723970, 2280330, 2972455, 3822500, 4857510, 6104560, 7596325, 9365400, 11450750, 13890760, 16731225, 20017060, 23801315, 28135800, 33081495

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,-4,-1,-1,4,4,-1,-1,-4,0,1,1,1,-1).

Formula

a(n) = 5*n*A256225(n).

G.f.: 5*x*(2*x^14 +19*x^13 +97*x^12 +277*x^11 +591*x^10 +955*x^9 +1267*x^8 +1355*x^7 +1217*x^6 +880*x^5 +520*x^4 +231*x^3 +75*x^2 +13*x +1) / ((x -1)^6*(x +1)^3*(x^2 +1)^2*(x^2 +x +1)^2).

Example

For n=2 there are 7 partitions of 5*2 = 10, so a(2) = 7*10 = 70.

Mathematica

Plus @@ Total /@ IntegerPartitions[5 #, {5}] & /@ Range[0, 31] (* Michael De Vlieger, Mar 20 2015 *)
CoefficientList[Series[5 x (2 x^14 + 19 x^13 + 97 x^12 + 277 x^11 + 591 x^10 + 955 x^9 + 1267 x^8 + 1355 x^7 + 1217 x^6 + 880 x^5 + 520 x^4 + 231 x^3 + 75 x^2 + 13 x + 1) / ((x - 1)^6 (x + 1)^3 (x^2 + 1)^2 (x^2 + x + 1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 20 2015 *)
LinearRecurrence[{1, 1, 1, 0, -4, -1, -1, 4, 4, -1, -1, -4, 0, 1, 1, 1, -1}, {0, 5, 70, 450, 1680, 4800, 11310, 23590, 44600, 78615, 130550, 207075, 315600, 465790, 667940, 935250, 1281520}, 40] (* Harvey P. Dale, Jun 14 2016 *)

Prog

(PARI) concat(0, Vec(5*x*(2*x^14 +19*x^13 +97*x^12 +277*x^11 +591*x^10 +955*x^9 +1267*x^8 +1355*x^7 +1217*x^6 +880*x^5 +520*x^4 +231*x^3 +75*x^2 +13*x +1) / ((x -1)^6*(x +1)^3*(x^2 +1)^2*(x^2 +x +1)^2) + O(x^100)))

Crossrefs

Cf. A235988, A238328, A256225, A256239.

Sequence in context: A286840 A034944 A064046 * A142588 A246154 A151471

Adjacent sequences: A256232 A256233 A256234 * A256236 A256237 A256238

Keyword

nonn,easy

Author

Colin Barker, Mar 20 2015

Status

approved