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A242551 Number of n-length words on infinite alphabet {1,2,...} such that the maximal runs of consecutive equal integers have lengths that are at least as great as the integer. 1
1, 1, 2, 5, 11, 24, 53, 118, 261, 577, 1276, 2823, 6246, 13819, 30572, 67635, 149630, 331029, 732344, 1620187, 3584388, 7929844, 17543415, 38811782, 85864379, 189960150, 420254129, 929739922, 2056889538, 4550514023, 10067228909, 22272010878, 49272989918, 109008007822, 241161451563, 533528195645 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
In other words, there is no restriction on the length of runs of 1's, the length of runs of 2's must be at least two, the length of runs of 3's must be at least three...
LINKS
EXAMPLE
a(3)=5 because we have: 111, 122, 221, 222, 333.
a(4)=11 because we have: 1111, 1122, 1221, 1222, 2211, 2221, 2222, 3331, 1333, 3333, 4444.
MAPLE
b:= proc(n, t) option remember; `if`(n=0, 1,
`if`(t=0, 0, b(n-1, t)) +add(
`if`(t=j, 0, b(n-j, j)), j=1..n))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..40); # Alois P. Heinz, Oct 07 2015
MATHEMATICA
n=nn=35; CoefficientList[Series[1/(1-Sum[v[i]/(1+v[i])/.v[i]->z^i/(1-z), {i, 1, n}]), {z, 0, nn}], z]
CROSSREFS
Sequence in context: A190512 A110513 A018115 * A018007 A295091 A071879
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, May 17 2014
STATUS
approved

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Last modified February 25 04:52 EST 2024. Contains 370310 sequences. (Running on oeis4.)