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

Author

David Neil McGrath, May 16 2015

Keywords

• nonn
• easy

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.

Examples

			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).
		

Links

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

Programs

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

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 *)

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

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).

Extensions

More terms from Vincenzo Librandi, May 19 2015