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URL: https://oeis.org/A213604

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A213604
Cumulative sums of digital roots of A005891(n).
1
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
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+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))) \\ G. C. Greubel, Feb 26 2017
CROSSREFS
Cf. A005891.
Sequence in context: A025021 A326767 A131439 * A374004 A102041 A232488
KEYWORD
nonn,base
AUTHOR
STATUS
approved