A199121 - OEIS

%I #5 Mar 30 2012 18:51:11

%S 1,1,0,0,1,2,2,2,2,2,3,4,4,4,4,5,6,6,7,8,7,8,10,11,11,12,14,14,15,17,

%T 18,20,21,22,24,25,27,30,31,32,35,37,39,41,44,45,48,52,53,56,60,62,66,

%U 69,72,76,81,86,89,92,96,103,109,113,117,123,127,134

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UlamSequence.html">Ulam Sequence</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Ulam_number">Ulam number</a>

%H <a href="/index/U#Ulam_num">Index entries for Ulam numbers</a>

%e The first terms of A003666 are 1, 4, 5, 6, 7, 8, 10, 16, 18, 19, ...

%e a(12) = #{8+4, 7+5, 7+4+1, 6+5+1} = 4;

%e a(13) = #{8+5, 8+4+1, 7+6, 7+5+1} = 4;

%e a(14) = #{10+4, 8+6, 8+5+1, 7+6+1} = 4;

%e a(15) = #{10+5, 10+4+1, 8+7, 8+6+1, 6+5+4} = 5;

%e a(16) = #{16, 10+6, 10+5+1, 8+7+1, 7+5+4, 6+5+4+1} = 6.

%o (Haskell)

%o a199121 = p a003666_list where

%o    p _  0 = 1

%o    p (u:us) m | m < u =

%o               | otherwise = p us (m - u) + p us m

%Y Cf. A000586; A199120, A199017, A199119, A199123.

%K nonn

%O 0,6

%A _Reinhard Zumkeller_, Nov 03 2011