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A257287
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a(n) = 6*7^n - 5*6^n.
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5
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1, 12, 114, 978, 7926, 61962, 472614, 3541578, 26190726, 191733162, 1392520614, 10049975178, 72163811526, 516030592362, 3677517616614, 26134444136778, 185292033880326, 1311149786699562, 9262681804120614, 65346572412186378
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OFFSET
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0,2
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COMMENTS
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First differences of 7^n - 6^n = A016169.
a(n-1) is the number of numbers with n digits having the largest digit equal to 6. Note that this is independent of the base b > 6.
Equivalently, number of n-letter words over a 7-letter alphabet {a,b,c,d,e,f,g}, which must not start with the first letter of the alphabet, and in which the last letter of the alphabet must appear.
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LINKS
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FORMULA
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G.f.: (1-x)/((1-6*x)*(1-7*x)).
a(n) = 13*a(n-1) - 42*a(n-2). (End)
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MATHEMATICA
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LinearRecurrence[{13, -42}, {1, 12}, 20] (* Harvey P. Dale, Dec 10 2023 *)
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PROG
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(PARI) a(n)=6*7^n-5*6^n
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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