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!)
A035699 Number of partitions of n into parts 8k+6 and 8k+7 with at least one part of each type. 82
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 3, 2, 3, 0, 1, 1, 3, 3, 6, 4, 5, 1, 3, 3, 7, 7, 11, 7, 8, 3, 7, 8, 15, 13, 19, 12, 13, 8, 16, 17, 27, 24, 30, 20, 23, 18, 32, 32, 46, 40, 48, 34, 41, 37, 56, 57, 76, 66, 76, 58, 71, 67, 97, 96, 122, 105, 119 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,21
LINKS
FORMULA
G.f.: (-1 + 1/Product_{k>=0} (1 - x^(8 k + 6)))*(-1 + 1/Product_{k>=0} (1 - x^(8 k + 7))). - Robert Price, Aug 16 2020
MATHEMATICA
nmax = 83; s1 = Range[0, nmax/8]*8 + 6; s2 = Range[0, nmax/8]*8 + 7;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 16 2020 *)
nmax = 83; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(8 k + 6)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(8 k + 7)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 2020*)
CROSSREFS
Sequence in context: A284264 A273302 A025086 * A132406 A197881 A332712
KEYWORD
nonn
AUTHOR
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 April 23 18:16 EDT 2024. Contains 371916 sequences. (Running on oeis4.)