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A049285 Restricted partitions.

%I A049285 #13 Jan 10 2014 10:36:44
%S A049285 0,0,0,0,1,1,2,4,7,13,24,43,78,141,253,455,818,1468,2637,4734,8495,
%T A049285 15247,27361,49094,88093,158063,283599,508840,912956,1638003,2938861,
%U A049285 5272795,9460227,16973125,30452380,54636174,98025512,175872397,315541228,566127763
%N A049285 Restricted partitions.
%C A049285 Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=5 and p(k) <= 2*p(k+1), see example.  [_Joerg Arndt_, Dec 18 2012]
%D A049285 Minc, H.; A problem in partitions: Enumeration of elements of a given degree in the free commutative entropic cyclic groupoid. Proc. Edinburgh Math. Soc. (2) 11 1958/1959 223-224.
%H A049285 Shimon Even & Abraham Lempel, <a href="http://dx.doi.org/10.1016/S0019-9958(72)90149-0">Generation and enumeration of all solutions of the characteristic sum condition</a>, Information and Control 21 (1972), 476-482.
%e A049285 From _Joerg Arndt_, Dec 18 2012: (Start)
%e A049285 There are a(10)=13 compositions 10=p(1)+p(2)+...+p(m) with p(1)=5 and p(k) <= 2*p(k+1):
%e A049285 [ 1]  [ 5 1 1 1 1 1 ]
%e A049285 [ 2]  [ 5 1 1 1 2 ]
%e A049285 [ 3]  [ 5 1 1 2 1 ]
%e A049285 [ 4]  [ 5 1 2 1 1 ]
%e A049285 [ 5]  [ 5 1 2 2 ]
%e A049285 [ 6]  [ 5 2 1 1 1 ]
%e A049285 [ 7]  [ 5 2 1 2 ]
%e A049285 [ 8]  [ 5 2 2 1 ]
%e A049285 [ 9]  [ 5 2 3 ]
%e A049285 [10]  [ 5 3 1 1 ]
%e A049285 [11]  [ 5 3 2 ]
%e A049285 [12]  [ 5 4 1 ]
%e A049285 [13]  [ 5 5 ]
%e A049285 (End)
%p A049285 v := proc(c,d) option remember; local i; if d < 0 or c < 0 then 0 elif d = c then 1 else add(v(i,d-c),i=1..2*c); fi; end; [ seq(v(5,n), n=1..50) ];
%t A049285 v[c_, d_] := v[c, d] = If[d < 0 || c < 0, 0, If[d == c, 1, Sum[v[i, d-c], {i, 1, 2*c}]]]; Table[v[5, n], {n, 1, 40}] (* _Jean-François Alcover_, Jan 10 2014, translated from Maple *)
%Y A049285 Cf. A002572, A002573, A049284, A002574.
%K A049285 nonn,easy
%O A049285 1,7
%A A049285 _N. J. A. Sloane_, Michael Somos