|
|
A025876
|
|
Expansion of 1/((1-x^5)*(1-x^6)*(1-x^7)).
|
|
6
|
|
|
1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 7, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 15, 15
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,13
|
|
COMMENTS
|
With a(0)=0, a(n) is the number of partitions of n into 4 parts whose largest part is twice the smallest part. - Wesley Ivan Hurt, Jan 06 2021
a(n) is the number of partitions of n into parts 5, 6, and 7. - Joerg Arndt, Jan 06 2021
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,1,1,0,0,0,-1,-1,-1,0,0,0,0,1).
|
|
FORMULA
|
a(n) = a(n-5) +a(n-6) +a(n-7) -a(n-11) -a(n-12) -a(n-13) +a(n-18). - Harvey P. Dale, Dec 16 2013
For n > 0, a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} [3*k = n-i-j], where [ ] is the Iverson bracket. - Wesley Ivan Hurt, Jan 06 2021
|
|
MATHEMATICA
|
CoefficientList[Series[1/((1-x^5)(1-x^6)(1-x^7)), {x, 0, 80}], x] (* or *)
LinearRecurrence[{0, 0, 0, 0, 1, 1, 1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 2, 1, 1, 1, 1, 2}, 80] (* Harvey P. Dale, Dec 16 2013 *)
|
|
PROG
|
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 80);
Coefficients(R!( 1/((1-x^5)*(1-x^6)*(1-x^7)) )); // G. C. Greubel, Nov 17 2022
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^5)*(1-x^6)*(1-x^7)) ).list()
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|