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.

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

Author

N. J. A. Sloane, Dec 06 2016

Keywords

• nonn

Links

• Joerg Arndt and N. J. A. Sloane, Counting Words that are in "Standard Order"

Crossrefs

A row of the array in A278987.

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)