login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A035641 Number of partitions of n into parts 6k and 6k+5 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 3, 0, 0, 0, 1, 3, 6, 0, 0, 1, 3, 7, 11, 0, 1, 3, 7, 14, 18, 1, 3, 7, 15, 25, 30, 3, 7, 15, 28, 44, 47, 7, 15, 29, 51, 72, 73, 15, 29, 54, 87, 116, 111, 29, 55, 94, 144, 180, 167, 55, 97, 159, 230, 276, 249, 98, 166, 259, 360 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,17

LINKS

Robert Price, Table of n, a(n) for n = 1..1000

FORMULA

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(6 k + 5)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - Robert Price, Aug 12 2020

MATHEMATICA

nmax = 75; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 5;

Table[Count[IntegerPartitions[n, All, s1~Join~s2],

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)

nmax = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035640, A035642-A035699.

Sequence in context: A218788 A328969 A027185 * A242434 A036873 A081130

Adjacent sequences:  A035638 A035639 A035640 * A035642 A035643 A035644

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 25 06:32 EDT 2020. Contains 337335 sequences. (Running on oeis4.)