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A256239
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Sum of all the parts in the partitions of 6n into 6 parts.
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3
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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
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OFFSET
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0,2
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LINKS
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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).
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FORMULA
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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).
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EXAMPLE
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For n=2 there are 11 partitions of 6*2 = 12, so a(2) = 11*12 = 132.
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MATHEMATICA
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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 *)
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PROG
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(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)))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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