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

1,3

Links

David Lovler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

Example

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

Prog

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

Crossrefs

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

Cf. A010888, A145389.

Cf. A005010, A030308.

Sequence in context: A217935 A100595 A107433 * A131417 A268135 A058369

Adjacent sequences: A090567 A090568 A090569 * A090571 A090572 A090573

Keyword

nonn,easy

Author

Giovanni Teofilatto, Feb 25 2004

Status

approved