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

0,2

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).

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)).

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 *)

Prog

(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

Crossrefs

Cf. A005891.

Sequence in context: A025021 A326767 A131439 * A374004 A102041 A232488

Adjacent sequences: A213601 A213602 A213603 * A213605 A213606 A213607

Keyword

nonn,base

Author

Alexander R. Povolotsky, Jun 15 2012

Status

approved