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%I M0071 N0023 #32 Aug 03 2022 08:55:08
%S 1,1,1,1,2,1,2,3,2,1,3,2,2,3,2,2,4,2,3,4,2,3,5,1,4,5,2,3,5,1,3,5,3,3,
%T 5,3,5,7,3,5,7,4,4,7,3,3,7,4,3,9,5,3,7,5,3,8,5,4,8,5,3,7,5,3,9,4,3,12,
%U 6,4,12,6,4,10,6,4,8,5,5,8,7,5,11,5,4
%N Number of decompositions of 2n into sum of 2 lucky numbers.
%C In general, a(3n-1) is larger than a(3n-2) and a(3n), which explains the bimodal nature of the graph. - _T. D. Noe_, Jan 29 2007
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D M. L. Stein and P. R. Stein, Tables of the Number of Binary Decompositions of All Even Numbers Less Than 200,000 into Prime Numbers and Lucky Numbers. Report LA-3106, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Sep 1964.
%H T. D. Noe, <a href="/A002850/b002850.txt">Table of n, a(n) for n = 1..10000</a>
%H V. Gardiner, R.Lazarus, N. Metropolis and S. Ulam, <a href="http://www.jstor.org/stable/3029719">On certain sequences of integers defined by sieves</a>, Math. Mag., 29 (1955), 117-119.
%t nmax = 1000;
%t luckies = Table[2i+1, {i, 0, nmax}]; For[n = 2, n < Length[luckies], r = luckies[[n++]]; luckies = ReplacePart[luckies, Table[r*i -> Nothing, {i, 1, Length[luckies]/r}]]];
%t a[n_] := IntegerPartitions[2n, {2}, luckies] // Length;
%t Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, Aug 03 2022, after _Robert Israel_ in A000959 *)
%Y Cf. A000959.
%K nonn,easy,nice
%O 1,5
%A _N. J. A. Sloane_
%E _Paul Zimmermann_ points out that the second term was incorrectly given as 2 in the Encyclopedia of Integer Sequences.
%E Missing a(71)-a(73) inserted by _Sean A. Irvine_, Nov 05 2014
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