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A199016 Number of partitions of n into terms of (1,2)-Ulam sequence, cf. A002858.

%I A199016 #7 Feb 16 2025 08:33:16
%S A199016 1,1,2,3,5,6,10,12,18,22,30,37,50,60,78,94,120,143,179,213,262,309,
%T A199016 376,440,531,618,737,855,1012,1167,1372,1575,1840,2104,2442,2783,3214,
%U A199016 3649,4193,4746,5430,6126,6980,7853,8914,10002,11311,12660,14274,15934
%N A199016 Number of partitions of n into terms of (1,2)-Ulam sequence, cf. A002858.
%H A199016 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A199016 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A199016 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%e A199016 The first terms of A002858 are 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, ...
%e A199016 a(6) = #{6, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, 1+1+1+1+1+1} = 10;
%e A199016 a(7) = #{6+1, 4+3, 4+2+1, 4+1+1+1, 3+3+1, 3+2+2, 3+2+1+1, 3+1+1+1+1, 2+2+2+1, 2+2+1+1+1, 2+1+1+1+1+1, 1+1+1+1+1+1+1} = 12.
%o A199016 (Haskell)
%o A199016 199016 = p a002858_list where
%o A199016    p _ 0 = 1
%o A199016    p us'@(u:us) m | m < u     = 0
%o A199016                   | otherwise = p us' (m - u) + p us m
%Y A199016 Cf. A000607; A199017, A199118, A199120, A199122.
%K A199016 nonn
%O A199016 0,3
%A A199016 _Reinhard Zumkeller_, Nov 03 2011