login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026812 Number of partitions of n in which the greatest part is 6. 16
0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 71, 90, 110, 136, 163, 199, 235, 282, 331, 391, 454, 532, 612, 709, 811, 931, 1057, 1206, 1360, 1540, 1729, 1945, 2172, 2432, 2702, 3009, 3331, 3692, 4070, 4494, 4935, 5427, 5942, 6510, 7104, 7760 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
Also number of partitions of n into 6 parts. - Washington Bomfim, Jan 15 2021
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 1..1000 from Vincenzo Librandi)
G. E. Andrews, Partitions: At the Interface of q-Series and Modular Forms, The Ramanujan Journal 7, 385-400 (2003), Eq.(3.10).
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1).
FORMULA
G.f.: x^6 / ((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)). - Colin Barker, Dec 20 2012
a(n) = A008284(n,6). - Robert A. Russell, May 13 2018
a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} 1. - Wesley Ivan Hurt, Jun 29 2019
a(n) = A001402(n) - A001401(n). a(n) = A001402(n-6). - Washington Bomfim, Jan 15 2021
a(n) = round((1/86400)*n^5 + (1/3840)*n^4 + (19/12960)*n^3 - (n mod 2)*(1/384)*n^2 + (1/17280)*b(n mod 6)*n), where b(0)=96, b(1)=b(5)=-629, b(2)=b(4)=-224, and b(3)=-309. - Washington Bomfim and Jon E. Schoenfield, Jan 16 2021
MATHEMATICA
Table[ Length[ Select[ Partitions[n], First[ # ] == 6 & ]], {n, 1, 60} ]
CoefficientList[Series[x^6/((1 - x) (1 - x^2) (1 - x^3) (1 - x^4) (1 - x^5) (1 - x^6)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)
Drop[LinearRecurrence[{1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1}, Append[Table[0, {20}], 1], 115], 14] (* Robert A. Russell, May 17 2018 *)
PROG
(PARI) my(x='x+O('x^99)); concat(vector(6), Vec(x^6/prod(k=1, 6, 1-x^k))) \\ Altug Alkan, May 17 2018
(PARI) a = vector(60, n, n--; round((n+11)*((6*n^4+249*n^3+2071*n^2 -4931*n+40621) /518400 +n\2*(n+10)/192+((n+1)\3+n\3*2)/54))); a = concat([0, 0, 0, 0, 0, 0], a) \\ Washington Bomfim, Jan 16 2021
(GAP) List([0..70], n->NrPartitions(n, 6)); # Muniru A Asiru, May 17 2018
CROSSREFS
Essentially same as A001402.
Sequence in context: A238659 A341870 A234666 * A001402 A008629 A347572
KEYWORD
nonn,easy,changed
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Jan 11 2002
a(0)=0 prepended by Seiichi Manyama, Jun 08 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 27 21:03 EST 2024. Contains 370378 sequences. (Running on oeis4.)