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

0,2

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).

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001622, A020714, A030308, A061047.

Sequence in context: A315306 A299986 A131501 * A315307 A315308 A315309

Adjacent sequences: A146948 A146949 A146950 * A146952 A146953 A146954

Keyword

nonn,easy

Author

Paul Curtz, Nov 03 2008

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

Status

approved