This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A105494 #5 Oct 03 2013 09:34:33
%S A105494 5,75,855,8665,83485,788515,7424515,70378930,675685240,6594991405,
%T A105494 65598204272
%N A105494 Number of partitions of {1,...,n} containing 4 strings of 3 consecutive integers such that only v-strings of consecutive integers can appear in a block, where v = 1,2,3.
%C A105494 Partitions enumerated by A105486 in which the maximal length of consecutive integers in a block is 3.
%D A105494 A. O. Munagi, Set Partitions with Successions and Separations, Int. J. Math and Math. Sc. 2005, no. 3 (2005), 451-463
%H A105494 A. O. Munagi, <a href="http://www.emis.de/journals/HOA/IJMMS/2005/3451.pdf">Set Partitions with Successions and Separations</a>,IJMMS 2005:3 (2005), 451-463.
%F A105494 a(n)=Sum(w(n, k, 4), k=1...n), where w(n, k, 4) is the case r=4 of w(n, k, r) given by w(m, k, r)=w(m-1, k-1, r)+(k-1)w(m-1, k, r)+w(m-2, k-1, r)+(k-1)w(m-2, k, r) +w(m-3, k-1, r-1)+(k-1)w(m-3, k, r-1) r=0, 1, ..., floor(n/3), k=1, 2, ..., n-2r, w(n, k, 0)=sum(binomial(n-j, j)*S2(n-j-1, k-1), j=0..floor(n/2)).
%e A105494 a(12)=5, the enumerated partitions are (1,2,3,7,8,9)(4,5,6,10,11,12),
%e A105494 (1,2,3,7,8,9)(4,5,6)(10,11,12), (1,2,3)(4,5,6,10,11,12)(7,8,9),
%e A105494 (1,2,3,10,11,12)(4,5,6)(7,8,9), (1,2,3)(4,5,6)(7,8,9) (10,11,12).
%Y A105494 Cf. A105486, A105490, A105493.
%K A105494 more,nonn
%O A105494 12,1
%A A105494 _Augustine O. Munagi_, Apr 11 2005