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 A049284 Restricted partitions. 6
 0, 0, 0, 1, 1, 2, 4, 7, 13, 24, 43, 78, 140, 251, 452, 812, 1457, 2617, 4697, 8428, 15126, 27142, 48700, 87384, 156787, 281307, 504723, 905562, 1624731, 2915039, 5230040, 9383505, 16835453, 30205347, 54192931, 97230224, 174445475, 312981054, 561534340, 1007475560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=4 and p(k) <= 2*p(k+1), see example.  [Joerg Arndt, Dec 18 2012] REFERENCES 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. LINKS Shimon Even and Abraham Lempel, Generation and enumeration of all solutions of the characteristic sum condition, Information and Control 21 (1972), 476-482. EXAMPLE From Joerg Arndt, Dec 18 2012: (Start) There are a(9)=13 compositions 9=p(1)+p(2)+...+p(m) with p(1)=4 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(4, 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}]]]; Table[v[4, n], {n, 1, 40}] (* Jean-François Alcover, Jan 10 2014, translated from Maple *) CROSSREFS Cf. A002572, A002573, A002574, A049285. Sequence in context: A069765 A090427 A006745 * A049285 A002843 A128742 Adjacent sequences:  A049281 A049282 A049283 * A049285 A049286 A049287 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Michael Somos STATUS approved

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