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 A055275 First differences of 9^n (A001019). 12
 1, 8, 72, 648, 5832, 52488, 472392, 4251528, 38263752, 344373768, 3099363912, 27894275208, 251048476872, 2259436291848, 20334926626632, 183014339639688, 1647129056757192, 14824161510814728, 133417453597332552, 1200757082375992968, 10806813741383936712, 97261323672455430408, 875351913052098873672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3,4,5,6,7,8,9} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6,7,8,9} we have f(x)<>y. - Aleksandar M. Janjic and Milan Janjic, Mar 27 2007 a(n) is the number of compositions of n when there are 8 types of each natural number. - Milan Janjic, Aug 13 2010 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets Index entries for linear recurrences with constant coefficients, signature (9). FORMULA G.f.: (1-x)/(1-9x). a(n) = 8*9^(n-1); a(0)=1. a(n) = 9a(n-1) + (-1)^n*C(1,1-n). E.g.f.: (1 + 8*exp(9*x))/9. - G. C. Greubel, Mar 16 2020 MAPLE 1, seq(8*9^(n-1), n=1..25); # G. C. Greubel, Mar 16 2020 MATHEMATICA q = 9; Join[{a = 1}, Table[If[n == 0, a = q*a - 1, a = q*a], {n, 0, 25}]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *) PROG (PARI) a(n)=if(n, 8*9^(n-1), 1) \\ Charles R Greathouse IV, Oct 07 2015 (MAGMA) [1] cat [8*9^(n-1): n in [1..25]]; // G. C. Greubel, Mar 16 2020 (Sage) [1]+[8*9^(n-1) for n in (1..25)] # G. C. Greubel, Mar 16 2020 CROSSREFS Cf. A001019. Sequence in context: A062541 A057091 A156566 * A155198 A147840 A115970 Adjacent sequences:  A055272 A055273 A055274 * A055276 A055277 A055278 KEYWORD easy,nonn AUTHOR Barry E. Williams, May 28 2000 STATUS approved

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Last modified September 19 02:53 EDT 2020. Contains 337175 sequences. (Running on oeis4.)