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 A002574 Restricted partitions. (Formerly M1070 N0404) 8
 0, 0, 1, 1, 2, 4, 7, 13, 24, 42, 76, 137, 245, 441, 792, 1420, 2550, 4576, 8209, 14732, 26433, 47424, 85092, 152670, 273914, 491453, 881744, 1581985, 2838333, 5092398, 9136528, 16392311, 29410243, 52766343, 94670652, 169853138, 304741614, 546751437, 980952673, 1759973660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=3 and p(k) <= 2*p(k+1), see example.  [Joerg Arndt, Dec 18 2012] REFERENCES Even, Shimon; Lempel, Abraham; Generation and enumeration of all solutions of the characteristic sum condition. Information and Control 21 (1972), 476-482. 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), pp. 223-224. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 H. Minc, 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. EXAMPLE From Joerg Arndt, Dec 18 2012: (Start) There are a(8)=13 compositions 8=p(1)+p(2)+...+p(m) with p(1)=3 and p(k) <= 2*p(k+1): [ 1]  [ 3 1 1 1 1 1 ] [ 2]  [ 3 1 1 1 2 ] [ 3]  [ 3 1 1 2 1 ] [ 4]  [ 3 1 2 1 1 ] [ 5]  [ 3 1 2 2 ] [ 6]  [ 3 2 1 1 1 ] [ 7]  [ 3 2 1 2 ] [ 8]  [ 3 2 2 1 ] [ 9]  [ 3 2 3 ] [10]  [ 3 3 1 1 ] [11]  [ 3 3 2 ] [12]  [ 3 4 1 ] [13]  [ 3 5 ] (End) MAPLE 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(3, n), n=1..50) ]; MATHEMATICA 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}]]]; a[n_] := v[3, n]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 05 2013, after Maple *) CROSSREFS Cf. A002572, A002573, A049284, A049285, A047913. Sequence in context: A005595 A296689 A096236 * A069765 A090427 A006745 Adjacent sequences:  A002571 A002572 A002573 * A002575 A002576 A002577 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Michael Somos STATUS approved

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Last modified October 18 03:19 EDT 2019. Contains 328135 sequences. (Running on oeis4.)