A008603 -id:A008603 - cp's OEIS frontend

A144608 Christoffel word of slope 10/11.

0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1

Offset: 0

N. J. A. Sloane, Jan 13 2009

The path is on the slope after 0, 21, 42, 63, 84,... steps (A008603), which gives the simple C-finite recurrence. - R. J. Mathar, May 28 2025

See A144595 for further details.

a(n) = a(n-21). - R. J. Mathar, May 28 2025

G.f.: -x^2*(1+x^2)*(x^8-x^6+x^4-x^2+1)*(x^4-x^3+x^2-x+1)*(1+x+x^2+x^3+x^4) / ( (x-1)*(1+x^6+x^5+x^4+x^3+x^2+x)*(1+x+x^2)*(1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12) ). - R. J. Mathar, May 28 2025

A242570 a(n) = 252 * n.

Original entry on oeis.org

0, 252, 504, 756, 1008, 1260, 1512, 1764, 2016, 2268, 2520, 2772, 3024, 3276, 3528, 3780, 4032, 4284, 4536, 4788, 5040, 5292, 5544, 5796, 6048, 6300, 6552, 6804, 7056, 7308, 7560, 7812, 8064, 8316, 8568, 8820, 9072, 9324, 9576, 9828, 10080, 10332, 10584, 10836, 11088, 11340

Offset: 0

Derek Orr, May 17 2014

As lcm(1,2,3,...,9) = 2520, 10*a(n) + k is divisible by each k from 1 through 9.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A001477, A008600, A008603, A008589, A008591, A008594, A008596.

Cf. A044102, A135628.

252*Range[0, 49] (* Alonso del Arte, May 17 2014 *)
LinearRecurrence[{2,-1},{0,252},50] (* Harvey P. Dale, Mar 25 2025 *)

PARI
```
for(n=0,50,print(252*n))
```

From Elmo R. Oliveira, Apr 16 2024: (Start)
G.f.: 252*x/(x-1)^2.
E.g.f.: 252*x*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2.
a(n) = 7*A044102(n) = 9*A135628(n) = 12*A008603(n) = 14*A008600(n) = 18*A008596(n) = 21*A008594(n) = 28*A008591(n) = 36*A008589(n) = 252*A001477(n). (End)

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A144608 Christoffel word of slope 10/11.

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A242570 a(n) = 252 * n.

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