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A199017 Number of partitions of n into distinct terms of (1,2)-Ulam sequence, cf. A002858.

%I A199017 #6 Feb 16 2025 08:33:16
%S A199017 1,1,1,2,2,2,3,3,3,4,4,5,5,6,7,7,8,9,10,11,12,13,14,14,16,16,17,19,20,
%T A199017 22,23,25,26,27,29,30,31,34,35,38,40,41,45,45,48,51,52,57,60,62,66,68,
%U A199017 71,75,78,83,86,93,97,100,107,109,115,120,124,132,138
%N A199017 Number of partitions of n into distinct terms of (1,2)-Ulam sequence, cf. A002858.
%H A199017 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A199017 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A199017 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%e A199017 The first terms of A002858 are 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, ...
%e A199017 a(10) = #{8+2, 6+4, 6+3+1, 4+3+2+1} = 4;
%e A199017 a(11) = #{11, 8+3, 8+2+1, 6+4+1, 6+3+2} = 5;
%e A199017 a(12) = #{11+1, 8+4, 8+3+1, 6+4+2, 6+3+2+1} = 5.
%o A199017 (Haskell)
%o A199017 a199017 = p a002858_list where
%o A199017    p _  0 = 1
%o A199017    p (u:us) m | m < u = 0
%o A199017               | otherwise = p us (m - u) + p us m
%Y A199017 Cf. A000586; A199016, A199119, A199121, A199123.
%K A199017 nonn
%O A199017 0,4
%A A199017 _Reinhard Zumkeller_, Nov 03 2011