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A257287 a(n) = 6*7^n - 5*6^n. 0
1, 12, 114, 978, 7926, 61962, 472614, 3541578, 26190726, 191733162, 1392520614, 10049975178, 72163811526, 516030592362, 3677517616614, 26134444136778, 185292033880326, 1311149786699562, 9262681804120614, 65346572412186378 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First differences of 7^n - 6^n = A016169.

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.

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (13,-42).

FORMULA

G.f.: (1-x)/((1-6*x)*(1-7*x)). - Vincenzo Librandi, May 04 2015

a(n) = 13*a(n-1) - 42*a(n-2). - Vincenzo Librandi, May 04 2015

MATHEMATICA

Table[6 7^n - 5 6^n, {n, 0, 30}] (* Vincenzo Librandi, May 04 2015 *)

PROG

(PARI) a(n)=6*7^n-5*6^n

(MAGMA) [6*7^n-5*6^n: n in [0..30]]; // Vincenzo Librandi, May 04 2015

CROSSREFS

Cf. A016169.

See also A000225, A027649, A255463, A257285 - A257289 and A088924.

Sequence in context: A055287 A080630 A005543 * A125400 A154237 A006635

Adjacent sequences:  A257284 A257285 A257286 * A257288 A257289 A257290

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, May 03 2015

STATUS

approved

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Last modified July 23 13:49 EDT 2019. Contains 325254 sequences. (Running on oeis4.)