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A254685
Number of partially ordered partitions of n into parts less than or equal to 3, in which the order of adjacent 2's and 3's is unimportant.
1
1, 1, 2, 4, 7, 12, 22, 39, 69, 123, 219, 389, 692, 1231, 2189, 3893, 6924, 12314, 21900, 38949, 69270, 123195, 219100, 389665, 693011, 1232506, 2191987, 3898404, 6933232, 12330612, 21929742, 39001599, 69363549, 123361658, 219396194, 390191659, 693947912
OFFSET
0,3
COMMENTS
Also number of compositions of n into parts 1, 2, 3, and 5.
FORMULA
G.f.: 1/(x^5 - x^3 - x^2 - x + 1).
a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-5).
EXAMPLE
a(7)=39. These are (331),(313),(133),(322=232=223),(3211=2311),(1123=1132),(1231=1321),(3112),(2113),(1312),(1213),(3121),(2131),(31111),(13111),(11311),(11131),(11113),(2221),(2212),(2122),(1222),(22111),(21211),(12211),(12121),(11221),(11212),(11122),(12112),(21112),(21121),(211111),(121111),(112111),(111211),(111121),(111112),(1111111).
MATHEMATICA
CoefficientList[Series[1/(x^5 - x^3 - x^2 - x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, May 06 2015 *)
PROG
(Magma) I:=[1, 2, 4, 7, 12]; [n le 5 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)-Self(n-5): n in [1..40]]; // Vincenzo Librandi, May 06 2015
CROSSREFS
Cf. A001399.
Sequence in context: A288996 A289153 A289019 * A002573 A288317 A064492
KEYWORD
nonn,easy
AUTHOR
David Neil McGrath, May 04 2015
EXTENSIONS
Corrected g.f. and more terms from Vincenzo Librandi, May 06 2015
a(0) added and g.f. adapted from Alois P. Heinz, May 08 2015
STATUS
approved