OFFSET
9,2
COMMENTS
The sequences in A089574 count ordered partitions. Sequence A001296 can be associated with 9 = 3+3+3. Six times sequence A005585, associated with 10 = 3+3+2+2. The other three sequences comprising A107600 are generated in A034261 and can be associated with 10 = 5 + 5 = 4 + 4 + 2 = 2 + 2 + 2 + 2 + 2.
LINKS
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
FORMULA
G.f.: (x^5 -5*x^4 +7*x^3 +4*x^2 -11*x -1) *x^9 /(x-1)^7. - Alois P. Heinz, Nov 06 2009
EXAMPLE
MAPLE
a:= n-> `if` (n<9, 0, (92292 +(-6580 +(-5745 +(1535 +(-147+5*n) *n) *n) *n) *n) *n /720 -218): seq(a(n), n=9..45); # Alois P. Heinz, Nov 06 2009
MATHEMATICA
Select[CoefficientList[Series[(x^5-5x^4+7x^3+4x^2-11x-1)x^9/(x-1)^7, {x, 0, 50}], x], #>0&] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 18, 101, 357, 978, 2274, 4711}, 42] (* Harvey P. Dale, May 01 2011 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Alford Arnold, May 17 2005
EXTENSIONS
More terms from Alois P. Heinz, Nov 06 2009
STATUS
approved