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A199118 Number of partitions of n into terms of (1,3)-Ulam sequence, cf. A002859.

%I A199118 #7 Feb 16 2025 08:33:16
%S A199118 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 A199118 276,322,379,442,518,600,698,803,931,1071,1231,1407,1615,1839,2099,
%U A199118 2384,2712,3069,3478,3923,4434,4991,5618,6303,7083,7928,8878,9916,11081
%N A199118 Number of partitions of n into terms of (1,3)-Ulam sequence, cf. A002859.
%H A199118 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A199118 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A199118 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%e A199118 The first terms of A002859 are 1, 3, 4, 5, 6, 8, 10, 12, 17, 21, ...
%e A199118 a(7) = #{6+1, 5+1+1, 4+3, 4+1+1+1, 3+3+1, 3+1+1+1+1, 7x1} = 7;
%e A199118 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 A199118 (Haskell)
%o A199118 a199118 = p a002859_list where
%o A199118    p _ 0 = 1
%o A199118    p us'@(u:us) m | m < u     = 0
%o A199118                   | otherwise = p us' (m - u) + p us m
%Y A199118 Cf. A000607; A199119, A199016, A199120, A199122.
%K A199118 nonn
%O A199118 0,4
%A A199118 _Reinhard Zumkeller_, Nov 03 2011