A256239 Sum of all the parts in the partitions of 6n into 6 parts.

0, 6, 132, 1044, 4776, 15960, 43416, 102144, 215712, 419040, 761520, 1310628, 2155752, 3412656, 5228076, 7784910, 11307648, 16068264, 22392504, 30666570, 41344080, 54953640, 72106452, 93504798, 119950416, 152353650, 191742720, 239273514, 296239776, 364083690

Offset: 0

Author

Colin Barker, Mar 20 2015

Keywords

• nonn
• easy

Examples

			For n=2 there are 11 partitions of 6*2 = 12, so a(2) = 11*12 = 132.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,3,-9,3,10,-10,-3,9,-3,-5,5,1,-3,1).

Crossrefs

Cf. A235988, A238328, A256225, A256235.

Programs

Mathematica

Plus @@ Total /@ IntegerPartitions[6 #, {6}] & /@ Range[0, 29] (* Michael De Vlieger, Mar 20 2015 *)
CoefficientList[Series[- 6 x (9 x^13 + 77 x^12 + 247 x^11 + 485 x^10 + 744 x^9 + 990 x^8 + 1109 x^7 + 1029 x^6 + 809 x^5 + 551 x^4 + 301 x^3 + 109 x^2 + 19 x + 1) / ((x - 1)^7 (x + 1)^2 (x^4 + x^3 + x^2 + x + 1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 20 2015 *)
LinearRecurrence[{3,-1,-5,5,3,-9,3,10,-10,-3,9,-3,-5,5,1,-3,1},{0,6,132,1044,4776,15960,43416,102144,215712,419040,761520,1310628,2155752,3412656,5228076,7784910,11307648},30] (* Harvey P. Dale, Mar 07 2025 *)

PARI

concat(0, Vec(-6*x*(9*x^13 +77*x^12 +247*x^11 +485*x^10 +744*x^9 +990*x^8 +1109*x^7 +1029*x^6 +809*x^5 +551*x^4 +301*x^3 +109*x^2 +19*x +1) / ((x -1)^7*(x +1)^2*(x^4 +x^3 +x^2 +x +1)^2) + O(x^100)))

Formula

a(n) = 6*n*A256226(n).

G.f.: -6*x*(9*x^13 +77*x^12 +247*x^11 +485*x^10 +744*x^9 +990*x^8 +1109*x^7 +1029*x^6 +809*x^5 +551*x^4 +301*x^3 +109*x^2 +19*x +1) / ((x -1)^7*(x +1)^2*(x^4 +x^3 +x^2 +x +1)^2).