cp's OEIS Frontend

A193748 Number of partitions of n into parts that are squares or triangular numbers (A005214).

%I A193748 #8 Jul 13 2013 12:04:14
%S A193748 1,1,1,2,3,3,5,6,7,10,13,14,19,23,26,33,41,45,56,67,76,91,108,120,143,
%T A193748 168,188,218,255,284,328,378,422,480,551,612,695,789,876,984,1115,
%U A193748 1233,1380,1549,1713,1907,2135,2349,2607,2902,3192,3524,3911,4287,4722
%N A193748 Number of partitions of n into parts that are squares or triangular numbers (A005214).
%H A193748 Reinhard Zumkeller, <a href="/A193748/b193748.txt">Table of n, a(n) for n = 0..100</a>
%e A193748 a(10) = #{10, 9+1, 6+4, 6+3+1, 6+1+1+1+1, 4+4+1+1, 4+3+3, 4+3+1+1+1, 4+6x1, 3+3+3+1, 3+3+1+1+1+1, 3+7x1, 10x1} = 13;
%e A193748 a(11) = #{10+1, 9+1+1, 6+4+1, 6+3+1+1, 6+1+1+1+1+1, 4+4+3, 4+4+1+1+1, 4+3+1+1+1+1, 4+7x1, 3+3+3+1+1, 3+3+5x1, 3+8x1, 11x1} = 14;
%e A193748 a(12) = #{10+1+1, 9+3, 9+1+1+1, 6+6, 6+4+1+1, 6+3+3, 6+3+1+1+1, 6+6x1, 4+4+4, 4+4+3+1, 4+4+1+1+1+1, 4+3+3+1+1, 4+3+5x1, 4+8x1, 3+3+3+3, 3+3+3+1+1+1, 3+3+6x1, 3+9x1, 12x1} = 19.
%o A193748 (Haskell)
%o A193748 a193748 = p a005214_list where
%o A193748    p _          0 = 1
%o A193748    p ks'@(k:ks) m
%o A193748      | m < k      = 0
%o A193748      | otherwise  = p ks' (m - k) + p ks m
%Y A193748 Cf. A000290, A000217, A001156, A007294, A193749, A000041.
%K A193748 nonn
%O A193748 0,4
%A A193748 _Reinhard Zumkeller_, Aug 03 2011