OFFSET
0,13
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, 0, -1, 1, 1, 1, 2, 0, 0, -1, -1, -1, -1, -3, 0, 0, 1, 1, 2, 2, 1, 1, 0, 0, -3, -1, -1, -1, -1, 0, 0, 2, 1, 1, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 1, 1, -1).
FORMULA
G.f.: x^10 / (Product_{k=1..10} 1-x^k ). - Colin Barker, Feb 22 2013
a(n) = A008284(n,10). - Robert A. Russell, May 13 2018
a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} 1. - Wesley Ivan Hurt, Jul 13 2019
MATHEMATICA
Table[ Length[ Select[ Partitions[n], First[ # ] == 10 & ]], {n, 1, 60} ]
CoefficientList[Series[x^10/((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) (1 - x^10)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)
PROG
(PARI) concat(vector(9), Vec(1/prod(k=1, 10, 1-x^k)+O(x^90))) \\ Charles R Greathouse IV, May 06 2015
(GAP) List([0..70], n->NrPartitions(n, 10)); # Muniru A Asiru, May 17 2018
(Magma) [#Partitions(k, 10): k in [1..51]]; // Marius A. Burtea, Jul 13 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(0)=0 prepended by Seiichi Manyama, Jun 08 2017
STATUS
approved