A055276 First differences of 11^n (A001020).

1, 10, 110, 1210, 13310, 146410, 1610510, 17715610, 194871710, 2143588810, 23579476910, 259374246010, 2853116706110, 31384283767210, 345227121439310, 3797498335832410, 41772481694156510, 459497298635721610, 5054470284992937710, 55599173134922314810, 611590904484145462910

Offset: 0

Author

Barry E. Williams, May 29 2000

Keywords

• easy
• nonn

Comments

a(n) is the number of compositions of n when there are 10 types of each natural number. - Milan Janjic, Aug 13 2010

Apart from the first term, number of monic squarefree polynomials over F_11 of degree n. - Charles R Greathouse IV, Feb 07 2012

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Milan Janjic, Enumerative Formulae for Some Functions on Finite Sets.
• Index entries for linear recurrences with constant coefficients, signature (11).

Crossrefs

Cf. A001020.

Programs

Mathematica

Table[EulerPhi[11^n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Nov 10 2009 *)

PARI

a(n)=round(11^n*10/11) \\ Charles R Greathouse IV, Feb 07 2012

Formula

a(n) = 11*a(n-1) + ((-1)^n)*C(1,1-n).

a(n) = 10*11^(n-1); a(0)=1.

G.f.: (1-x)/(1-11*x).

E.g.f.: (10*exp(11*x) + 1)/11. - Elmo R. Oliveira, Mar 18 2025

Extensions

More terms from Elmo R. Oliveira, Mar 25 2025