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%I #6 Mar 30 2012 18:51:11
%S 1,1,1,2,3,4,6,7,10,13,17,21,28,34,42,52,65,78,96,113,138,165,196,231,
%T 276,322,379,442,518,600,698,803,931,1071,1231,1407,1615,1839,2099,
%U 2384,2712,3069,3478,3923,4434,4991,5618,6303,7083,7928,8878,9916,11081
%N Number of partitions of n into terms of (1,3)-Ulam sequence, cf. A002859.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%e The first terms of A002859 are 1, 3, 4, 5, 6, 8, 10, 12, 17, 21, ...
%e a(7) = #{6+1, 5+1+1, 4+3, 4+1+1+1, 3+3+1, 3+1+1+1+1, 7x1} = 7;
%e a(8) = #{8, 6+1+1, 5+3, 5+1+1+1, 4+4, 4+3+1, 4+1+1+1+1, 3+3+1+1, 3+1+1+1+1+1, 8x1} = 10.
%o (Haskell)
%o a199118 = p a002859_list where
%o p _ 0 = 1
%o p us'@(u:us) m | m < u = 0
%o | otherwise = p us' (m - u) + p us m
%Y Cf. A000607; A199119, A199016, A199120, A199122.
%K nonn
%O 0,4
%A _Reinhard Zumkeller_, Nov 03 2011
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