Search: id:A000991
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%I A000991 M2554 N1011
%S A000991 1,3,6,12,21,40,67,117,193,319,510,818,1274,1983,3032,4610,6915,
%T A000991 10324,15235,22371,32554,47119,67689,96763,137404,194211,272939,381872
%N A000991 Number of 3-line partitions of n.
%D A000991 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000991 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000991 L. Carlitz, Generating functions and partition problems, pp. 144-169 
               of A. L. Whiteman, ed., Theory of Numbers, Proc. Sympos. Pure Math., 
               8 (1965). Amer. Math. Soc., see p. 145, eq. (1.8).
%D A000991 M. S. Cheema and B. Gordon, Some remarks on two- and three-line partitions, 
               Duke Math. J., 31 (1964), 267-273.
%D A000991 P. A. MacMahon, The connexion between the sum of the squares of the divisors 
               and the number of partitions of a given number, Messenger Math., 
               54 (1924), 113-116.
%F A000991 G.f.: prod from k =1 to inf ( 1 - x^k )^(-3) / ( 1 - x )^2 ( 1 - x^2 
               ).
%Y A000991 Cf. A000990.
%Y A000991 Sequence in context: A087503 A133627 A092176 this_sequence A095093 A139422 
               A062483
%Y A000991 Adjacent sequences: A000988 A000989 A000990 this_sequence A000992 A000993 
               A000994
%K A000991 nonn
%O A000991 1,2
%A A000991 N. J. A. Sloane (njas(AT)research.att.com).

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