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!)
A068980 Number of partitions of n into nonzero tetrahedral numbers. 22
1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 11, 11, 12, 12, 15, 15, 16, 16, 19, 19, 22, 22, 25, 25, 28, 29, 32, 32, 35, 36, 42, 42, 45, 46, 52, 53, 56, 57, 63, 64, 70, 71, 77, 78, 84, 87, 94, 95, 101, 104, 115, 116, 122, 125, 136, 139, 146, 149, 160, 163, 175 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Zhicheng Gao, Andrew MacFie and Daniel Panario, Counting words by number of occurrences of some patterns, The Electronic Journal of Combinatorics, 18 (2011), #p143.

FORMULA

G.f.: 1 / prod(k>=3, 1 - z^binomial(k, 3) ).

G.f.: Sum_{i>=0} x^(i*(i+1)*(i+2)/6) / Product_{j=1..i} (1 - x^(j*(j+1)*(j+2)/6)). - Ilya Gutkovskiy, Jun 08 2017

EXAMPLE

a(10)=4 because we can write 10 = 10 = 4 + 4 + 1 + 1 = 4 + 1 + 1 + 1 + 1 + 1 = 1 + ... + 1.

MATHEMATICA

nmax = 100; CoefficientList[Series[Product[1/(1-x^(k*(k+1)*(k+2)/6)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 09 2017 *)

CROSSREFS

See also A007294 (partitions into triangular numbers), A000292 (tetrahedral numbers).

Cf. A226748, A003108.

Sequence in context: A091372 A185322 A324918 * A280950 A279135 A053266

Adjacent sequences:  A068977 A068978 A068979 * A068981 A068982 A068983

KEYWORD

easy,nonn

AUTHOR

Franklin T. Adams-Watters, Apr 01 2002

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 29 06:29 EDT 2020. Contains 337425 sequences. (Running on oeis4.)