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 A257285 a(n) = 4*5^n - 3*4^n. 5
 1, 8, 52, 308, 1732, 9428, 50212, 263348, 1365892, 7026068, 35916772, 182729588, 926230852, 4681485908, 23608756132, 118849087028, 597466660612, 3000218204948, 15052630632292, 75469311591668, 378171191679172, 1894154493279188, 9483966605929252 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First differences of 5^n - 4^n = A005060. Number of numbers with n digits having the largest digit equal to 4. Note that this is independent of the base b>4. Equivalently, number of n-letter words over a 5-letter alphabet {a,b,c,d,e}, which must not start with the first letter of the alphabet, and in which the last letter of the alphabet must appear. LINKS Index entries for linear recurrences with constant coefficients, signature (9,-20). FORMULA G.f.: (1-x)/((1-4*x)*(1-5*x)). - Vincenzo Librandi, May 04 2015 a(n) = 9*a(n-1) - 20*a(n-2). - Vincenzo Librandi, May 04 2015 MATHEMATICA Table[4 5^n - 3 4^n, {n, 0, 30}] (* Vincenzo Librandi, May 04 2015 *) PROG (PARI) a(n)=4*5^n-3*4^n (MAGMA) [4*5^n-3*4^n: n in [0..30]]; // Vincenzo Librandi, May 04 2015 CROSSREFS Cf. A005060. See also A000225, A027649, A255463, A257286 - A257289 and A088924. Sequence in context: A153336 A080279 A279283 * A125345 A111996 A016129 Adjacent sequences:  A257282 A257283 A257284 * A257286 A257287 A257288 KEYWORD nonn,easy AUTHOR M. F. Hasler, May 03 2015 STATUS approved

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Last modified April 21 20:40 EDT 2019. Contains 322328 sequences. (Running on oeis4.)