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 A000715 Number of partitions of n, with three kinds of 1,2 and 3 and two kinds of 4,5,6,.... (Formerly M2786 N1121) 2
 1, 3, 9, 22, 50, 104, 208, 394, 724, 1286, 2229, 3769, 6253, 10176, 16303, 25723, 40055, 61588, 93647, 140875, 209889, 309846, 453565, 658627, 949310, 1358589, 1931464, 2728547, 3831654, 5350119, 7430158, 10265669, 14113795, 19313168, 26309405, 35685523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution of A000712 and A001399. - 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..10000 N. J. A. Sloane, Transforms FORMULA EULER transform of 3, 3, 3, 2, 2, 2, 2, 2, ... G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*Product_{k>=1}(1-x^k)^2). - Emeric Deutsch, Apr 17 2006 a(n) ~ exp(2*Pi*sqrt(n/3)) * n^(1/4) / (8 * 3^(1/4) * Pi^3). - 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 g:=1/((1-x)*(1-x^2)*(1-x^3)*product((1-x^k)^2, k=1..40)): gser:=series(g, x=0, 40): seq(coeff(gser, x, n), n=0..31); # Emeric Deutsch, Apr 17 2006 # second Maple program a:= proc(n) a(n):= `if`(n=0, 1, add(add(d*`if`(d<4, 3, 2), d=numtheory [divisors](j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..50); # Alois P. Heinz, Sep 25 2012 MATHEMATICA nn=25; p=Product[1/(1- x^i)^2, {i, 1, nn}]; CoefficientList[Series[p /(1-x)/(1-x^2)/(1-x^3), {x, 0, nn}], x] (* Geoffrey Critzer, Sep 25 2012 *) CROSSREFS Sequence in context: A001937 A086817 A247188 * A260545 A034505 A143099 Adjacent sequences:  A000712 A000713 A000714 * A000716 A000717 A000718 KEYWORD nonn AUTHOR EXTENSIONS Extended with formula from Christian G. Bower, Apr 15 1998 STATUS approved

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Last modified January 23 16:29 EST 2022. Contains 350514 sequences. (Running on oeis4.)