A257934 Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7).

1, 1, 2, 4, 8, 14, 26, 48, 89, 163, 300, 552, 1016, 1868, 3436, 6320, 11625, 21381, 39326, 72332, 133040, 244698, 450070, 827808, 1522577, 2800455, 5150840, 9473872, 17425168, 32049880, 58948920, 108423968, 199422769, 366795657, 674642394, 1240860820, 2282298872, 4197802086, 7720961778

Offset

0,3

Comments

This sequence counts partially ordered partitions of (n) into parts (1,2,3,4) in which the position (order) of the 4's are unimportant. For example the permutations of (43421) are counted as permutations of (321)=6.

Links

Table of n, a(n) for n=0..38.

Index entries for related partition-counting sequences

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

G.f.: 1 / ((x-1)*(x+1)*(x^2+1)*(x^3+x^2+x-1)). - Colin Barker, May 17 2015

Example

a(6)=26; these are (42=24),(411=141=114),(33),(321=six),(3111=four),(222),(2211=six),(21111=five),(111111).

Prog

(PARI) Vec(1 / ((x-1)*(x+1)*(x^2+1)*(x^3+x^2+x-1)) + O(x^100)) \\ Colin Barker, May 17 2015

Crossrefs

Cf. A258000, A257863.

Sequence in context: A135491 A164154 A164156 * A258000 A164155 A164167

Adjacent sequences: A257931 A257932 A257933 * A257935 A257936 A257937

Keyword

nonn,easy

Author

David Neil McGrath, May 13 2015

Extensions

Missing term (6320) inserted by Colin Barker, May 17 2015

Status

approved