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A055275 First differences of 9^n (A001019). 11
1, 8, 72, 648, 5832, 52488, 472392, 4251528, 38263752, 344373768, 3099363912, 27894275208, 251048476872, 2259436291848, 20334926626632, 183014339639688, 1647129056757192, 14824161510814728, 133417453597332552, 1200757082375992968, 10806813741383936712 (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

Table of n, a(n) for n=0..20.

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (9).

EXAMPLE

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).

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

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 June 28 11:48 EDT 2017. Contains 288822 sequences.