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A199123 Number of partitions of n into distinct terms of (2,3)-Ulam sequence, cf. A001857.

%I A199123 #6 Feb 16 2025 08:33:16
%S A199123 1,0,1,1,0,2,0,2,2,2,3,2,3,3,4,4,5,5,6,6,6,8,8,9,11,10,12,14,12,17,16,
%T A199123 17,22,19,24,25,25,30,30,33,37,37,42,45,46,52,54,57,64,66,69,79,76,87,
%U A199123 93,91,109,105,115,126,123,140,144,151,166,169,180,193
%N A199123 Number of partitions of n into distinct terms of (2,3)-Ulam sequence, cf. A001857.
%H A199123 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A199123 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A199123 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%e A199123 The first terms of A001857 are 2, 3, 5, 7, 8, 9, 13, 14, 18, 19, 24, ...
%e A199123 a(20) = #{18+2, 13+7, 13+5+2, 9+8+3, 8+7+5, 8+7+3+2} = 6;
%e A199123 a(21) = #{19+2, 18+3, 14+7, 14+5+2, 13+8, 13+5+3, 9+7+5, 9+7+3+2} = 8.
%o A199123 (Haskell)
%o A199123 a199123 = p a001857_list where
%o A199123    p _  0 = 1
%o A199123    p (u:us) m | m < u = 0
%o A199123               | otherwise = p us (m - u) + p us m
%Y A199123 Cf. A000586; A199122, A199017, A199119, A199121.
%K A199123 nonn
%O A199123 0,6
%A A199123 _Reinhard Zumkeller_, Nov 03 2011