A090570 Numbers that are congruent to {0, 1} mod 9.

0, 1, 9, 10, 18, 19, 27, 28, 36, 37, 45, 46, 54, 55, 63, 64, 72, 73, 81, 82, 90, 91, 99, 100, 108, 109, 117, 118, 126, 127, 135, 136, 144, 145, 153, 154, 162, 163, 171, 172, 180, 181, 189, 190, 198, 199, 207, 208, 216, 217, 225, 226

Offset: 1

Author

Giovanni Teofilatto, Feb 25 2004

Keywords

• nonn
• easy

Examples

			13 is 1101 in base 2, so a(13+1) = a(14) = 36*1 + 18*1 + 9*0 + 1*1 = 36+18+1 = 55. - _Philippe Deléham_, Oct 17 2011
		

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Union of A008591 and A017173. - Reinhard Zumkeller, Oct 10 2008

Cf. A010888, A145389.

Cf. A005010, A030308.

Programs

PARI

forstep(n=0,200,[1,8],print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

Formula

A145389(a(n)) = A010888(a(n)). - Reinhard Zumkeller, Oct 10 2008

a(n) = 9*n - a(n-1) - 17 (with a(1)=0). - Vincenzo Librandi, Nov 16 2010

From R. J. Mathar, Oct 08 2011: (Start)

a(n) = 9*n/2 - 25/4 - 7*(-1)^n/4.

G.f.: x^2*(1+8*x)/( (1+x)*(1-x)^2 ). (End)

a(n+1) = Sum_{k>=0} A030308(n,k)*A005010(k-1), with A005010(-1)=1. - Philippe Deléham, Oct 17 2011.

E.g.f.: 8 + ((18*x - 25)*exp(x) - 7*exp(-x))/4. - David Lovler, Sep 03 2022