OFFSET
0,2
COMMENTS
REFERENCES
H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 122.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
M. A. Harrison, On the number of classes of binary matrices, IEEE Transactions on Computers, C-22.12 (1973), 1048-1052. (Annotated scanned copy)
N. J. A. Sloane, Transforms
FORMULA
EULER transform of 3, 3, 3, 3, 2, 2, 2, 2, ...
G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*Product_{k>=1} (1 - x^k)^2).
a(n) ~ exp(2*Pi*sqrt(n/3)) * 3^(1/4) * n^(3/4) / (32*Pi^4). - Vaclav Kotesovec, Aug 18 2015
EXAMPLE
a(2)=9 because we have 2, 2', 2", 1+1, 1'+1', 1"+1", 1+1', 1+1", 1'+1".
MAPLE
with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:= etr(n-> `if`(n<5, 3, 2)): seq(a(n), n=0..40); # Alois P. Heinz, Sep 08 2008
MATHEMATICA
nn=31; CoefficientList[Series[1/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/Product[(1-x^i)^2, {i, 1, nn}], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 28 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Extended with formula from Christian G. Bower, Apr 15 1998
Edited by Emeric Deutsch, Mar 22 2005
STATUS
approved