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A193749 Number of partitions of n into distinct parts that are squares or triangular numbers (A005214). 3

%I #8 Jul 13 2013 12:04:14

%S 1,1,0,1,2,1,1,2,1,2,4,2,1,4,4,3,5,4,3,7,7,4,6,7,6,10,10,5,10,14,10,

%T 12,14,9,14,20,13,13,20,17,18,24,17,16,27,26,22,27,25,26,35,31,26,35,

%U 37,36,42,37,35,48,47,40,49,49,48,60,58,49,61,66,61

%N Number of partitions of n into distinct parts that are squares or triangular numbers (A005214).

%H Reinhard Zumkeller, <a href="/A193749/b193749.txt">Table of n, a(n) for n = 0..250</a>

%e a(10) = #{10, 9+1, 6+4, 6+3+1} = 4;

%e a(11) = #{10+1, 6+4+1} = 2;

%e a(12) = #{9+3} = 1;

%e a(13) = #{10+3, 9+4, 9+3+1, 6+4+3} = 4.

%o (Haskell)

%o a193749 = p a005214_list where

%o p _ 0 = 1

%o p (k:ks) m

%o | m < k = 0

%o | otherwise = p ks (m - k) + p ks m

%Y Cf. A000290, A000217, A033461, A024940, A193748, A000009.

%K nonn

%O 0,5

%A _Reinhard Zumkeller_, Aug 03 2011

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)