A146951 Numbers that are congruent to 0 or 6 mod 10.

0, 6, 10, 16, 20, 26, 30, 36, 40, 46, 50, 56, 60, 66, 70, 76, 80, 86, 90, 96, 100, 106, 110, 116, 120, 126, 130, 136, 140, 146, 150, 156, 160, 166, 170, 176, 180, 186, 190, 196, 200, 206, 210, 216, 220, 226, 230, 236, 240, 246, 250, 256, 260, 266, 270, 276, 280

Offset: 0

Author

Paul Curtz, Nov 03 2008

Keywords

• nonn
• easy

Comments

Rank of terms of A061047 ending in with 0.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A001622, A020714, A030308, A061047.

Programs

Magma

I:=[0, 6, 10]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]]; // Vincenzo Librandi, May 18 2012

Mathematica

CoefficientList[Series[x*(6+4*x)/((1-x)^2*(1+x)),{x,0,50}],x] (* Vincenzo Librandi, May 18 2012 *)

Formula

a(n) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=6 and b(k) = 5*2^k = A020714(k) for k > 0. - Philippe Deléham, Oct 18 2011

From Colin Barker, May 15 2012: (Start)

a(n) = 1/2 - (-1)^n/2 + 5*n.

a(n) = a(n-1) + a(n-2) - a(n-3).

G.f.: x*(6+4*x)/((1-x)^2*(1+x)). (End)

E.g.f.: 5*x*exp(x) + sinh(x). - Stefano Spezia, May 14 2021

Sum_{n>=1} (-1)^(n+1)/a(n) = log(5)/8 - sqrt(1-2/sqrt(5))*Pi/20 - log(phi)/(4*sqrt(5)), where phi is the golden ratio (A001622). - Amiram Eldar, Sep 15 2022

Extensions

Replaced definition by a comment from Philippe Deléham, Oct 18 2011. Afer the change this becomes a list, but it is better to keep the offset as 0. - N. J. A. Sloane, Sep 08 2022