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 A002573 Restricted partitions. (Formerly M1062 N0399) 9
 0, 1, 1, 2, 4, 7, 12, 22, 39, 70, 126, 225, 404, 725, 1299, 2331, 4182, 7501, 13458, 24145, 43316, 77715, 139430, 250152, 448808, 805222, 1444677, 2591958, 4650342, 8343380, 14969239, 26856992, 48185362, 86451602, 155106844, 278284440, 499283177, 895787396, 1607174300, 2883507098 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=2 and p(k) <= 2*p(k+1), see example. [Joerg Arndt, Dec 18 2012] REFERENCES 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..500 Shimon Even & Abraham Lempel, Generation and enumeration of all solutions of the characteristic sum condition, Information and Control 21 (1972), 476-482. 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)=22 compositions 8=p(1)+p(2)+...+p(m) with p(1)=2 and p(k) <= 2*p(k+1): [ 1]  [ 2 1 1 1 1 1 1 ] [ 2]  [ 2 1 1 1 1 2 ] [ 3]  [ 2 1 1 1 2 1 ] [ 4]  [ 2 1 1 2 1 1 ] [ 5]  [ 2 1 1 2 2 ] [ 6]  [ 2 1 2 1 1 1 ] [ 7]  [ 2 1 2 1 2 ] [ 8]  [ 2 1 2 2 1 ] [ 9]  [ 2 1 2 3 ] [10]  [ 2 2 1 1 1 1 ] [11]  [ 2 2 1 1 2 ] [12]  [ 2 2 1 2 1 ] [13]  [ 2 2 2 1 1 ] [14]  [ 2 2 2 2 ] [15]  [ 2 2 3 1 ] [16]  [ 2 2 4 ] [17]  [ 2 3 1 1 1 ] [18]  [ 2 3 1 2 ] [19]  [ 2 3 2 1 ] [20]  [ 2 3 3 ] [21]  [ 2 4 1 1 ] [22]  [ 2 4 2 ] (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(2, 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[2, n]; Table[a[n], {n, 1, 35}] (* Jean-François Alcover, Jan 30 2012, after Maple *) CROSSREFS Cf. A002572, A047913, A002574, A049284, A049285. A column of the triangle in A176431. Sequence in context: A289153 A289019 A254685 * A288317 A064492 A000072 Adjacent sequences:  A002570 A002571 A002572 * A002574 A002575 A002576 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)