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A321773
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Number of compositions of n into parts with distinct multiplicities and with exactly three parts.
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5
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1, 3, 6, 4, 9, 9, 10, 12, 15, 13, 18, 18, 19, 21, 24, 22, 27, 27, 28, 30, 33, 31, 36, 36, 37, 39, 42, 40, 45, 45, 46, 48, 51, 49, 54, 54, 55, 57, 60, 58, 63, 63, 64, 66, 69, 67, 72, 72, 73, 75, 78, 76, 81, 81, 82, 84, 87, 85, 90, 90, 91, 93, 96, 94, 99, 99
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OFFSET
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3,2
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LINKS
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FORMULA
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G.f.: x^3*(1 + 3*x + 5*x^2) / ((1 - x)^2*(1 + x)*(1 + x + x^2)).
a(n) = a(n-2) + a(n-3) - a(n-5) for n>7.
(End)
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EXAMPLE
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Also the number of 3-part non-strict compositions of n. For example, the a(3) = 1 through a(11) = 15 triples are:
111 112 113 114 115 116 117 118 119
121 122 141 133 161 144 181 155
211 131 222 151 224 171 226 191
212 411 223 233 225 244 227
221 232 242 252 262 272
311 313 323 333 334 335
322 332 414 343 344
331 422 441 424 353
511 611 522 433 434
711 442 443
622 515
811 533
551
722
911
(End)
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MATHEMATICA
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Table[Length[Join@@Permutations/@Select[IntegerPartitions[n, {3}], !UnsameQ@@#&]], {n, 0, 100}] (* Gus Wiseman, Nov 11 2020 *)
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CROSSREFS
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A235451 counts 3-part compositions with distinct run-lengths
A001399(n-6) counts 3-part compositions in the complement.
A261982 counts non-strict compositions of any length.
A032020 counts strict compositions.
A242771 counts triples that are not strictly increasing.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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