%I A053445
%S A053445 1,0,1,0,2,0,3,1,4,2,7,3,10,7,14,11,22,17,32,28,45,43,67,63,95,96,
%T A053445 134,139,192,199,269,287,373,406,521,566,718,792,983,1092,1346,1496,
%U A053445 1827,2045,2465,2772,3323,3733,4449,5016,5929,6696,7882,8897,10426
%N A053445 Second differences of partition numbers A000041.
%C A053445 First differences of 0 1 1 2 2 4 4 7 8 12 14 21 24 34 41 55... (A002865).
%C A053445 For n>2, a(n-2) is the number of partitions of n with all parts > 1 and 
               with the largest part occurring more than once. The list of partitions 
               counted begins 22 (so a(2) = 1); 33, 222 (so a(4) = 2); 44, 332, 
               2222 (so a(6) = 3); 333; 55, 442, 3322, 22222; 443, 3332; 66, 552, 
               444, 4422, 3333, 33222, 222222; 553, 4432, 33322; ...
%C A053445 a(n) is the number of certain level-n quasi-primary states of a quotient 
               space of certain Verma modules. See the Furlan et al. reference p. 
               67. - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), 
               Apr 25 2003
%D A053445 P. Furlan, G. M. Sotkov and I. T. Todorov, Two-Dimensional Conformal 
               Quantum Field Theory, Rivista d. Nuovo Cimento 12, 6 (1989) 1-202.
%D A053445 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 115, 3.
%H A053445 T. D. Noe, <a href="b053445.txt">Table of n, a(n) for n=0..1000</a>
%e A053445 a(8) = 7 - 4 = 3; the corresponding partitions are 44, 332 and 2222
%t A053445 Table[(PartitionsP[n+2]-PartitionsP[n+1])-(PartitionsP[n+1]-PartitionsP[n]),
               {n,0,42}] - Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 23 2008
%o A053445 (MAGMA) m:=58; S:=[ NumberOfPartitions(n): n in [0..m] ]; [ S[n+2]-2*S[n+1]+S[n]: 
               n in [1..m-2] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Jun 09 2009]
%Y A053445 Cf. A000041, A002865, A072380, A081094, A081095.
%Y A053445 Sequence in context: A084964 A008720 A008734 this_sequence A162517 A162170 
               A008798
%Y A053445 Adjacent sequences: A053442 A053443 A053444 this_sequence A053446 A053447 
               A053448
%K A053445 easy,nice,nonn
%O A053445 0,5
%A A053445 Alford Arnold (Alford1940(AT)aol.com), Jan 12 2000
%E A053445 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 02 2000
%E A053445 Start of sequence changed Apr 25 2003