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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) 8
 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 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((1-x^k)^2, k=1..infinity)]. 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: A034505 A143099 A160462 * A278668 A160526 A121589 Adjacent sequences:  A000708 A000709 A000710 * A000712 A000713 A000714 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 April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)