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A137740 Number of different strings of length n+5 obtained from "123...n" by iteratively duplicating any substring. 12
1, 32, 138, 348, 700, 1246, 2050, 3188, 4749, 6836, 9567, 13076, 17514, 23050, 29872, 38188, 48227, 60240, 74501, 91308, 110984, 133878, 160366, 190852, 225769, 265580, 310779, 361892, 419478, 484130, 556476, 637180, 726943, 826504, 936641, 1058172, 1191956 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See A137743 for comments and examples.
LINKS
FORMULA
a(n) = (n+4)(n^2+3n-8)(n^2+23n+150)/5!+4 for n>4.
G.f.: x*(x^8+2*x^7-7*x^6-20*x^5+57*x^4-20*x^3-39*x^2+26*x+1) / (x-1)^6. - Colin Barker, Nov 04 2013
MATHEMATICA
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 32, 138, 348, 700, 1246, 2050, 3188, 4749}, 40] (* Harvey P. Dale, Oct 18 2020 *)
PROG
(PARI) A137740(n)=if(n<2, 1, n=A135473(n+5, n); n[ #n]) /* function A135473 defined in A137743 */
(PARI) A137740(n)=if(n>4, n*(n*(n*(n*(n+30)+315)+1110)-136)/5!-36, [1, 32, 138, 348][n])
CROSSREFS
Sequence in context: A299386 A299185 A299946 * A221597 A159763 A100164
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Feb 10 2008
EXTENSIONS
More terms from Colin Barker, Nov 04 2013
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)