|
Search: id:A005003
|
|
|
| A005003 |
|
Number of rhyme schemes (see reference for precise definition).
(Formerly M4416)
|
|
+0
4
|
|
| 1, 7, 35, 156, 670, 2886, 12797, 59537, 294585, 1562324, 8900568, 54346140, 353937741, 2444771767, 17814457447, 136308242144, 1091001532590, 9105746802826, 79041398643849, 711994012088297, 6642697774712213
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
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.
|
|
LINKS
|
J. Riordan, Cached copy of paper
|
|
FORMULA
|
a(k)=1. a(n)=k*a(n-1)+A000110(n-1)-A102661(n-1,k-2), k=3. - R. J. Mathar, Jul 15 2008
|
|
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) ;
|
|
CROSSREFS
|
Sequence in context: A000588 A005285 A006095 this_sequence A037099 A055421 A110213
Cf. A005002, A127021.
Adjacent sequences: A005000 A005001 A005002 this_sequence A005004 A005005 A005006
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms from R. J. Mathar, Jul 15 2008
|
|
|
Search completed in 0.002 seconds
|
