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A256315 Number of partitions of 3n into exactly 6 parts. 5
0, 0, 1, 3, 11, 26, 58, 110, 199, 331, 532, 811, 1206, 1729, 2432, 3331, 4494, 5942, 7760, 9975, 12692, 15944, 19858, 24473, 29941, 36308, 43752, 52327, 62239, 73551, 86499, 101155, 117788, 136479, 157532, 181038, 207338, 236534, 269005, 304865, 344534 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Also the number of partitions of 3*(n-2) into at most 6 parts. - Colin Barker, Apr 01 2015
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,2,1,-4,3,3,-4,1,2,-4,1,2,-1).
FORMULA
G.f.: x^2*(x^8+x^7+4*x^6+5*x^5+5*x^4+5*x^3+4*x^2+x+1) / ((x-1)^6*(x+1)^3*(x^2+1)*(x^4+x^3+x^2+x+1)).
EXAMPLE
For n=3 the 3 partitions of 3*3 = 9 are [1,1,1,1,1,4], [1,1,1,1,2,3] and [1,1,1,2,2,2].
MATHEMATICA
CoefficientList[Series[x^2*(x^8 + x^7 + 4*x^6 + 5*x^5 + 5*x^4 + 5*x^3 + 4*x^2 + x + 1)/((x - 1)^6*(x + 1)^3*(x^2 + 1)*(x^4 + x^3 + x^2 + x + 1)), {x, 0, 50}], x] (* Wesley Ivan Hurt, Feb 22 2017 *)
Table[Length@ IntegerPartitions[3 n, {6}], {n, 0, 40}] (* Michael De Vlieger, Feb 22 2017 *)
PROG
(PARI) concat(0, vector(40, n, k=0; forpart(p=3*n, k++, , [6, 6]); k))
(PARI) concat([0, 0], Vec(x^2*(x^8+x^7+4*x^6+5*x^5+5*x^4+5*x^3+4*x^2+x+1) / ((x-1)^6*(x+1)^3*(x^2+1)*(x^4+x^3+x^2+x+1)) + O(x^100)))
CROSSREFS
Sequence in context: A211811 A011942 A220147 * A290513 A101612 A123928
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 23 2015
STATUS
approved

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Last modified May 23 14:50 EDT 2024. Contains 372763 sequences. (Running on oeis4.)