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A278988
a(n) is the number of words of length n over an alphabet of size 3 that are in standard order and which have the property that every letter that appears in the word is repeated.
1
0, 0, 1, 1, 4, 11, 41, 162, 610, 2165, 7327, 23948, 76352, 239175, 739909, 2268710, 6912430, 20966441, 63390587, 191220048, 575888044, 1732382363, 5207108161, 15642295562, 46970926394, 141005053341, 423208097431, 1270026944852, 3810919694680, 11434503913775, 34307135619197
OFFSET
0,5
FORMULA
Conjectures from Colin Barker, Nov 25 2017: (Start)
G.f.: x^2*(1 - 9*x + 34*x^2 - 71*x^3 + 100*x^4 - 97*x^5 + 52*x^6 - 12*x^7) / ((1 - x)^3*(1 - 2*x)^2*(1 - 3*x)).
a(n) = (2*(3+3^n) - 3*(2+2^n)*n + 6*n^2) / 12 for n>3.
a(n) = 10*a(n-1) - 40*a(n-2) + 82*a(n-3) - 91*a(n-4) + 52*a(n-5) - 12*a(n-6) for n>9.
(End)
CROSSREFS
A row of the array in A278987.
Sequence in context: A306188 A307702 A214167 * A214188 A214239 A278989
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 06 2016
STATUS
approved