cp's OEIS Frontend

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

%I A193749 #8 Jul 13 2013 12:04:14
%S A193749 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 A193749 12,14,9,14,20,13,13,20,17,18,24,17,16,27,26,22,27,25,26,35,31,26,35,
%U A193749 37,36,42,37,35,48,47,40,49,49,48,60,58,49,61,66,61
%N A193749 Number of partitions of n into distinct parts that are squares or triangular numbers (A005214).
%H A193749 Reinhard Zumkeller, <a href="/A193749/b193749.txt">Table of n, a(n) for n = 0..250</a>
%e A193749 a(10) = #{10, 9+1, 6+4, 6+3+1} = 4;
%e A193749 a(11) = #{10+1, 6+4+1} = 2;
%e A193749 a(12) = #{9+3} = 1;
%e A193749 a(13) = #{10+3, 9+4, 9+3+1, 6+4+3} = 4.
%o A193749 (Haskell)
%o A193749 a193749 = p a005214_list where
%o A193749    p _      0    = 1
%o A193749    p (k:ks) m
%o A193749      | m < k     = 0
%o A193749      | otherwise = p ks (m - k) + p ks m
%Y A193749 Cf. A000290, A000217, A033461, A024940, A193748, A000009.
%K A193749 nonn
%O A193749 0,5
%A A193749 _Reinhard Zumkeller_, Aug 03 2011