OFFSET
0,12
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 1..1000 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 2, 1, 1, 1, 0, -1, -1, -1, -2, -1, -1, 1, 1, 2, 1, 1, 1, 0, -1, -1, -1, -2, 0, 1, 0, 0, 1, 0, 1, 0, 0, -1, -1, 1).
FORMULA
G.f.: x^9 / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^8)*(1-x^9)). - Colin Barker, Feb 22 2013
a(n) = A008284(n,9). - Robert A. Russell, May 13 2018
MAPLE
part_ZL:=[S, {S=Set(U, card=r), U=Sequence(Z, card>=1)}, unlabeled]: seq(count(subs(r=9, part_ZL), size=m), m=1..50); # Zerinvary Lajos, Mar 09 2007
MATHEMATICA
Table[ Length[ Select[ Partitions[n], First[ # ] == 9 & ]], {n, 1, 60} ]
CoefficientList[Series[x^9/((1 - x) (1 - x^2) (1 - x^3) (1 - x^4) (1 - x^5) (1 - x^6) (1 - x^7) (1 - x^8) (1 - x^9)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)
Drop[LinearRecurrence[{1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 2, 1, 1, 1, 0, -1, -1, -1, -2, -1, -1, 1, 1, 2, 1, 1, 1, 0, -1, -1, -1, -2, 0, 1, 0, 0, 1, 0, 1, 0, 0, -1, -1, 1}, Append[Table[0, {44}], 1], 136], 35] (* Robert A. Russell, May 17 2018 *)
PROG
(PARI) x='x+O('x^99); concat(vector(9), Vec(x^9/prod(k=1, 9, 1-x^k))) \\ Altug Alkan, May 17 2018
(GAP) List([0..70], n->NrPartitions(n, 9)); # Muniru A Asiru, May 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(0)=0 prepended by Seiichi Manyama, Jun 08 2017
STATUS
approved