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A000711 Number of partitions of n, with three kinds of 1,2,3 and 4 and two kinds of 5,6,7,...
(Formerly M2787 N1122)
9
1, 3, 9, 22, 51, 107, 217, 416, 775, 1393, 2446, 4185, 7028, 11569, 18749, 29908, 47083, 73157, 112396, 170783, 256972, 383003, 565961, 829410, 1206282, 1741592, 2497425, 3557957, 5037936, 7091711, 9927583, 13823626, 19151731, 26404879, 36236988, 49509149 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Convolution of A000712 and A001400. - Vaclav Kotesovec, Aug 18 2015
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
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
Sequence in context: A143099 A365664 A160462 * A278668 A365665 A160526
KEYWORD
nonn
AUTHOR
EXTENSIONS
Extended with formula from Christian G. Bower, Apr 15 1998
Edited by Emeric Deutsch, Mar 22 2005
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)