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

Author

David Neil McGrath, May 04 2015

Keywords

• nonn
• easy

Comments

Also number of compositions of n into parts 1, 2, 3, and 5.

Examples

			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).
		

Links

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

Crossrefs

Cf. A001399.

Programs

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

Mathematica

CoefficientList[Series[1/(x^5 - x^3 - x^2 - x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, May 06 2015 *)

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).

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