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A199119 Number of partitions of n into distinct terms of (1,3)-Ulam sequence, cf. A002859.

%I A199119 #6 Feb 16 2025 08:33:16
%S A199119 1,1,0,1,2,2,2,2,3,4,4,4,5,6,6,7,7,8,10,9,9,12,13,13,13,14,17,18,18,
%T A199119 19,21,23,25,26,27,30,33,33,36,40,42,43,45,51,55,55,57,62,67,71,72,76,
%U A199119 82,87,91,95,100,107,112,116,124,132,137,143,151,159,170
%N A199119 Number of partitions of n into distinct terms of (1,3)-Ulam sequence, cf. A002859.
%H A199119 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A199119 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A199119 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%e A199119 The first terms of A002859 are 1, 3, 4, 5, 6, 8, 10, 12, 17, 21, ...
%e A199119 a(10) = #{10, 6+4, 6+3+1, 5+4+1} = 4;
%e A199119 a(11) = #{10+1, 8+3, 6+5, 6+4+1} = 4;
%e A199119 a(12) = #{12, 8+4, 8+3+1, 6+5+1, 5+4+3} = 5.
%o A199119 (Haskell)
%o A199119 a199119 = p a002859_list where
%o A199119    p _  0 = 1
%o A199119    p (u:us) m | m < u = 0
%o A199119               | otherwise = p us (m - u) + p us m
%Y A199119 A000586; A199118, A199017, A199121, A199123.
%K A199119 nonn
%O A199119 0,5
%A A199119 _Reinhard Zumkeller_, Nov 03 2011