|
|
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>4, n*(n*(n*(n*(n+30)+315)+1110)-136)/5!-36, [1, 32, 138, 348][n])
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|