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!)
A306094 Number of plane partitions of n where parts are colored in (at most) 4 colors. 6
1, 4, 36, 228, 1540, 8964, 56292, 316388, 1857028, 10301892, 57884132, 312915172, 1720407492, 9132560068, 48898964964, 256790538660, 1350883911620, 6992031608260, 36296271612324, 185785685287076, 952221494828996, 4831039856692356, 24489621255994276 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(0) = 1 corresponds to the empty sum, in which all terms are colored in one among four given colors, since there is no term at all.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..50

FORMULA

a(n) = Sum_{k=1..n} A091298(n,k)*4^k.

EXAMPLE

For n = 1, there is only the partition [1], which can be colored in any of the four colors, whence a(1) = 4.

For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 4 + 16 + 16 = 36 distinct possibilities.

PROG

(PARI) a(n)=!n+sum(k=1, n, A091298(n, k)*4^k)

CROSSREFS

Cf. A091298, A208447.

Column 4 of A306100 and A306101. See A306099 and A306093 for columns 2 and 3.

Sequence in context: A074434 A257888 A197424 * A018217 A003488 A295411

Adjacent sequences:  A306091 A306092 A306093 * A306095 A306096 A306097

KEYWORD

nonn

AUTHOR

M. F. Hasler, Sep 22 2018

EXTENSIONS

a(12) corrected and a(13)-a(22) added by Alois P. Heinz, Sep 24 2018

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 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)