A213604 Cumulative sums of digital roots of A005891(n).

1, 7, 14, 18, 24, 28, 35, 41, 42, 48, 55, 59, 65, 69, 76, 82, 83, 89, 96, 100, 106, 110, 117, 123, 124, 130, 137, 141, 147, 151, 158, 164, 165, 171, 178, 182, 188, 192, 199, 205, 206, 212, 219, 223, 229, 233, 240, 246, 247, 253, 260, 264, 270, 274, 281, 287

Offset: 0

Author

Alexander R. Povolotsky, Jun 15 2012

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A005891.

Programs

Mathematica

CoefficientList[Series[(1 + 6*x + 7*x^2 + 4 x^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)), {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 *)

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

Formula

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.

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)).