A213604 - OEIS

%I #16 Feb 27 2017 02:55:56

%S 1,7,14,18,24,28,35,41,42,48,55,59,65,69,76,82,83,89,96,100,106,110,

%T 117,123,124,130,137,141,147,151,158,164,165,171,178,182,188,192,199,

%U 205,206,212,219,223,229,233,240,246,247,253,260,264,270,274,281,287

%N Cumulative sums of digital roots of A005891(n).

%H G. C. Greubel, <a href="/A213604/b213604.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,1,-1).

%F a(n+9) = -a(n) + a(n+1) + a(n+8), a(0)=1, a(1)=7, a(2)=14, a(3)=18, a(4)=24, a(5)=28, a(6)=35, a(7)=41, a(8)=42.

%F G.f.: (1+6*x+7*x^2+4x^3+6*x^4+4*x^5+7*x^6+6*x^7) / ((x-1)^2 * (1+x+x^2+x^3+x^4+x^5+x^6+x^7)).

%t CoefficientList[Series[(1 + 6*x + 7*x^2 + 4 x^3 + 6*x^4 + 4*x^5 + 7*x^6 +

%t 6*x^7)/((x - 1)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)), {x, 0, 50}], x] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,1,-1}, {1,7,14,18,24, 28,35,41,42}, 50](* _G. C. Greubel_, Feb 26 2017 *)

%o (PARI) x='x+O('x^50); Vec((1+6*x+7*x^2+4x^3+6*x^4+4*x^5+7*x^6+6*x^7) / ((x-1)^2 * (1+x+x^2+x^3+x^4+x^5+x^6+x^7))) \\ _G. C. Greubel_, Feb 26 2017

%Y Cf. A005891.

%K nonn,base

%O 0,2

%A _Alexander R. Povolotsky_, Jun 15 2012