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A240844 Number of partitions of n into tribonacci numbers (cf. A000073).

%I A240844 #4 Apr 13 2014 10:30:58
%S A240844 1,1,2,2,4,4,6,7,10,11,14,16,20,23,28,32,38,43,50,56,65,73,83,92,105,
%T A240844 116,131,144,163,178,199,217,242,263,291,316,348,377,413,447,488,527,
%U A240844 573,617,670,720,779,835,903,966,1041,1112,1198,1277,1371,1460,1566
%N A240844 Number of partitions of n into tribonacci numbers (cf. A000073).
%e A240844 a(6) = #{4+2, 4+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, 6x1} = 6;
%e A240844 a(7) = #{7, 4+2+1, 4+1+1+1, 2+2+2+1, 2+2+1+1+1, 2+1+1+1+1+1, 7x1} = 7;
%e A240844 a(8) = #{7+1, 4+4, 4+2+2, 4+2+1+1, 4+1+1+1+1, 2+2+2+2, 2+2+2+1+1, 2+2+1+1+1+1, 2+6x1, 8x1} = 10;
%e A240844 a(9) = #{7+2, 7+1+1, 4+4+1, 4+2+2+1, 4+2+1+1+1, 4+5x1, 2+2+2+2+1, 2+2+2+1+1+1, 2+2+5x1, 2+7x1, 9x1} = 11;
%e A240844 a(10) = #{7+2+1, 7+1+1+1, 4+4+2, 4+4+1+1, 4+2+2+2, 4+2+2+1+1, 4+2+1+1+1+1, 4+6x1, 5x2, 2+2+2+2+1+1, 2+2+2+1+1+1+1, 2+2+6x1, 2+8x1, 10x1} = 14.
%o A240844 (Haskell)
%o A240844 a240844 = p $ drop 3 a000073_list where
%o A240844    p _          0 = 1
%o A240844    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%Y A240844 Cf. A117546.
%K A240844 nonn
%O A240844 0,3
%A A240844 _Reinhard Zumkeller_, Apr 13 2014