Search: id:A011970
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%I A011970
%S A011970 1,4,8,15,37,114,409,1657,7432,36401,192713,1094076,6618379,42436913,
%T A011970 287151994,2042803419,15229360185,118645071202,963494800557,
%U A011970 8138047375093,71351480138824,648222594284197,6092330403828749
%N A011970 Apply (1+Shift)^3 to Bell numbers.
%C A011970 Starting with n=3 (a(3)=15), number of set partitions of n+2 with at 
               least one singleton and the smallest element in any singleton is 
               exactly n-2. The maximum number of singletons is therefore 5. Alternatively, 
               starting with n=3, number of set partitions of n+2 with at least 
               one singleton and the largest element in any singleton is exactly 
               5. - Olivier GERARD (olivier.gerard(AT)gmail.com), Oct 29 2007
%C A011970 Let V(N)={v(1),v(2),...,v(N)} denote an ordered set of increasing positive 
               integers containing 3 pairs of adjacent elements that differ by at 
               least 2, that is, v(i),v(i+1) with v(i+1)-v(i)>1. Then for n>2, a(n) 
               is the number of partitions of V(n+1) into blocks of nonconsecutive 
               integers. - Augustine O. Munagi (amunagi(AT)yahoo.com), Jul 17 2008
%D A011970 Olivier Gerard and Karol Penson, A budget of set partitions statistics, 
               in preparation.
%D A011970 A. O. Munagi, Extended set partitions with successions, European J. Combin. 
               29(5) (2008), 1298--1308.
%F A011970 If n>2, then bell(n)+3*bell(n-1)+3*bell(n-2)+bell(n-3). - Augustine O. 
               Munagi (amunagi(AT)yahoo.com), Jul 17 2008
%e A011970 a(3)=15 because the set {1,3,5,7} has 15 different partitions which are 
               necessarily into blocks of nonconsecutive integers.
%p A011970 with(combinat): 1,4,8,seq(`if`(n>2,bell(n)+3*bell(n-1)+3*bell(n-2)+bell(n-3),
               NULL),n=3..22); - Augustine O. Munagi (amunagi(AT)yahoo.com), Jul 
               17 2008
%Y A011970 Cf. A000110.
%Y A011970 Cf. A011968, A011969.
%Y A011970 Sequence in context: A027961 A018921 A103536 this_sequence A111988 A110652 
               A059373
%Y A011970 Adjacent sequences: A011967 A011968 A011969 this_sequence A011971 A011972 
               A011973
%K A011970 nonn
%O A011970 0,2
%A A011970 N. J. A. Sloane (njas(AT)research.att.com).

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