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!)
A035638 Number of partitions of n into parts 6k and 6k+2 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 4, 0, 4, 0, 4, 0, 10, 0, 11, 0, 11, 0, 22, 0, 25, 0, 26, 0, 44, 0, 51, 0, 54, 0, 84, 0, 98, 0, 105, 0, 152, 0, 178, 0, 193, 0, 266, 0, 312, 0, 341, 0, 452, 0, 528, 0, 581, 0, 749, 0, 873, 0, 964, 0, 1214, 0, 1409, 0, 1561, 0, 1930, 0, 2234 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

LINKS

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

FORMULA

G.f. : (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - Robert Price, Aug 12 2020

MATHEMATICA

nmax = 76; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 2;

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

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

nmax = 76; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 12 2020 *)

CROSSREFS

Cf. A035441-A035468, A035618-A035637, A035639-A035699.

Sequence in context: A246130 A010675 A035673 * A292142 A098002 A241658

Adjacent sequences:  A035635 A035636 A035637 * A035639 A035640 A035641

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 May 12 23:09 EDT 2021. Contains 343829 sequences. (Running on oeis4.)