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A199120 Number of partitions of n into terms of (1,4)-Ulam sequence, cf. A003666.

%I A199120 #10 Feb 16 2025 08:33:16
%S A199120 1,1,1,1,2,3,4,5,7,8,11,13,17,20,25,30,38,44,54,63,77,90,107,124,148,
%T A199120 171,202,231,271,310,360,412,477,542,622,705,809,915,1042,1175,1335,
%U A199120 1501,1699,1905,2148,2403,2702,3018,3383,3768,4212,4682,5223,5794,6445
%N A199120 Number of partitions of n into terms of (1,4)-Ulam sequence, cf. A003666.
%H A199120 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>
%H A199120 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>
%H A199120 <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>
%e A199120 The first terms of A003666 are 1, 4, 5, 6, 7, 8, 10, 16, 18, 19, ...
%e A199120 a(7) = #{7, 6+1, 5+1+1, 4+1+1+1, 7x1} = 5;
%e A199120 a(8) = #{8, 7+1, 6+1+1, 5+1+1+1, 4+4, 4+1+1+1+1, 8x1} = 7;
%e A199120 a(9) = #{8+1, 7+1+1, 6+1+1+1, 5+4, 5+1+1+1+1, 4+4+1, 4+5x1, 9x1} = 8.
%o A199120 (Haskell)
%o A199120 a199120 = p a003666_list where
%o A199120    p _ 0 = 1
%o A199120    p us'@(u:us) m | m < u     = 0
%o A199120                   | otherwise = p us' (m - u) + p us m
%Y A199120 Cf. A000607; A199016, A199118, A199121, A199122.
%K A199120 nonn
%O A199120 0,5
%A A199120 _Reinhard Zumkeller_, Nov 03 2011