A258000 Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7-x^9).

1, 1, 2, 4, 8, 14, 26, 48, 89, 164, 302, 557, 1028, 1896, 3496, 6448, 11893, 21935, 40455, 74613, 137613, 253807, 468108, 863354, 1592327, 2936808, 5416499, 9989915, 18424893, 33981939, 62674564, 115593785, 213195313, 393206621, 725210344, 1337541166

Offset

0,3

Comments

This sequence counts partially ordered partitions of (n) into parts (1,2,3,4) in which only the position (order) of the 1's are important. The 1's behave as placeholders for unordered 2's,3's and 4's.

Links

Table of n, a(n) for n=0..35.

Index entries for partition-counting sequences

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

Formula

a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7) + a(n-9)

G.f.: 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7-x^9).

Example

a(6)=26; these are (42,24=one),(411),(141),(114),(33),(321,231=one),(123,132=one),(312),(213),(3111=four),(222),(2211),(1122),(2112),(1221),(1212),(2121),(21111=five),(111111).

Mathematica

LinearRecurrence[{1, 1, 1, 1, -1, -1, -1, 0, 1}, {1, 1, 2, 4, 8, 14, 26, 48, 89}, 50] (* Vincenzo Librandi, May 19 2015 *)

Prog

(PARI) Vec(1/(-x^9+x^7+x^6+x^5-x^4-x^3-x^2-x+1) + O(x^100)) \\ Colin Barker, May 17 2015
(Magma) I:=[1, 1, 2, 4, 8, 14, 26, 48, 89]; [n le 9 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)+Self(n-4)-Self(n-5)-Self(n-6)-Self(n-7)+Self(n-9): n in [1..40]]; // Vincenzo Librandi, May 19 2015

Crossrefs

Sequence in context: A164154 A164156 A257934 * A164155 A164167 A164169

Adjacent sequences: A257997 A257998 A257999 * A258001 A258002 A258003

Keyword

nonn,easy

Author

David Neil McGrath, May 16 2015

Extensions

More terms from Vincenzo Librandi, May 19 2015

Status

approved