A005003 Number of rhyme schemes (see reference for precise definition).
1, 7, 35, 156, 670, 2886, 12797, 59537, 294585, 1562324, 8900568, 54346140, 353937741, 2444771767, 17814457447, 136308242144, 1091001532590, 9105746802826, 79041398643849, 711994012088297, 6642697774712213
Offset: 1
Keywords
References
- J. Riordan, A budget of rhyme scheme counts, pp. 455 - 465 of Second International Conference on Combinatorial Mathematics, New York, April 4-7, 1978. Edited by Allan Gewirtz and Louis V. Quintas. Annals New York Academy of Sciences, 319, 1979.
- 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
- J. Riordan, Cached copy of paper
Programs
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Maple
(Maple program from R. J. Mathar): A000110 := proc(n) combinat[bell](n) ; end: A102661 := proc(n,k) add(combinat[stirling2](n,i),i=1..k) ; end: A005001:=n->if n = 0 then 0; else add(combinat[bell](k),k=0..n); fi; beta := proc(n,k) if k= 1 then A005001(n) ; elif k= n then 1 ; else k*beta(n-1,k)+A000110(n-1)-A102661(n-1,k-2) ; fi ; end: A005003 := proc(n) beta(n,3) ; end: seq(A005003(n),n=3..30) ;
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Mathematica
a[1] = 1; a[n_] := 3*a[n-1] + BellB[n+1] - StirlingS2[n+1, 1]; a /@ Range[21] (* Jean-François Alcover, May 20 2011, after R. J. Mathar *)
Formula
Extensions
More terms from R. J. Mathar, Jul 15 2008