OFFSET
0,10
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, -1, 0, 1, 1, 2, 0, 0, 0, -2, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, -1, 1).
FORMULA
G.f.: x^7 / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)). - Colin Barker, Feb 22 2013
a(n) = A008284(n,7). - Robert A. Russell, May 13 2018
a(n) = A008636(n-7). - R. J. Mathar, Feb 13 2019
a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3} Sum_{i=j..floor((n-j-k-l-m-o)/2)} 1. - Wesley Ivan Hurt, Jun 30 2019
MATHEMATICA
Table[ Length[ Select[ Partitions[n], First[ # ] == 7 & ]], {n, 1, 60} ]
CoefficientList[Series[x^7/((1 - x) (1 - x^2) (1 - x^3) (1 - x^4) (1 - x^5) (1 - x^6) (1 - x^7)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)
Drop[LinearRecurrence[{1, 1, 0, 0, -1, 0, -1, -1, 0, 1, 1, 2, 0, 0, 0, -2, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, -1, 1}, Append[Table[0, {27}], 1], 121], 20] (* Robert A. Russell, May 17 2018 *)
PROG
(PARI) x='x+O('x^99); concat(vector(7), Vec(x^7/prod(k=1, 7, 1-x^k))) \\ Altug Alkan, May 17 2018
(GAP) List([0..70], n->NrPartitions(n, 7)); # Muniru A Asiru, May 17 2018
(Magma) [#Partitions(n, 7): n in [0..53]]; // Marius A. Burtea, Jul 01 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Jan 11 2002
a(0)=0 prepended by Seiichi Manyama, Jun 08 2017
STATUS
approved