A146951 - OEIS

%I #45 Sep 15 2022 02:21:09

%S 0,6,10,16,20,26,30,36,40,46,50,56,60,66,70,76,80,86,90,96,100,106,

%T 110,116,120,126,130,136,140,146,150,156,160,166,170,176,180,186,190,

%U 196,200,206,210,216,220,226,230,236,240,246,250,256,260,266,270,276,280

%N Numbers that are congruent to 0 or 6 mod 10.

%C Rank of terms of A061047 ending in with 0.

%H Vincenzo Librandi, <a href="/A146951/b146951.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F 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

%F From _Colin Barker_, May 15 2012: (Start)

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

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

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

%F E.g.f.: 5*x*exp(x) + sinh(x). - _Stefano Spezia_, May 14 2021

%F 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

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

%o (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

%Y Cf. A001622, A020714, A030308, A061047.

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Nov 03 2008

%E 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