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, 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.

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,-1).

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

Adjacent sequences: A254682 A254683 A254684 * A254686 A254687 A254688

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