login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A160974 Number of partitions of n where every part appears at least 4 times. 4
1, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 4, 2, 4, 4, 7, 5, 8, 7, 13, 10, 13, 12, 21, 18, 22, 21, 34, 29, 40, 36, 55, 48, 63, 64, 88, 79, 100, 99, 139, 125, 160, 155, 207, 199, 241, 241, 314, 302, 369, 366, 466, 454, 550, 557, 690, 679, 807, 821, 1016, 1001, 1180, 1207, 1460, 1466, 1708 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms  n=1..967 from R. H. Hardin)

FORMULA

G.f.: Product_{j>=1} (1+x^(4*j)/(1-x^j)). - Emeric Deutsch, Jun 24 2009

a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 - exp(-x) + exp(-4*x)) dx = -0.903005550655893892139378653023287247062261773608753265529... . - Vaclav Kotesovec, Jan 05 2016

EXAMPLE

a(12) = 4 because we have 3333, 2^6, 22221111, and 1^(12). - Emeric Deutsch, Jun 24 2009

MAPLE

g := product(1+x^(4*j)/(1-x^j), j = 1..30): gser := series(g, x = 0, 85): seq(coeff(gser, x, n), n = 0..66); # Emeric Deutsch, Jun 24 2009

# second Maple program:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(b(n-i*j, i-1), j=[0, $4..iquo(n, i)])))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..80);  # Alois P. Heinz, Oct 02 2017

MATHEMATICA

nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(4*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)

CROSSREFS

Cf. A007690, A100405, A160975-A160990.

Sequence in context: A161079 A161295 A161270 * A187718 A029196 A051493

Adjacent sequences:  A160971 A160972 A160973 * A160975 A160976 A160977

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 01 2009

EXTENSIONS

Initial terms changed to match b-file. - N. J. A. Sloane, Aug 31 2009

Maple program fixed by Vaclav Kotesovec, Nov 28 2015

a(0)=1 prepended by Alois P. Heinz, Oct 02 2017

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 December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)