A135304 -id:A135304 - cp's OEIS frontend

0, 1, 11, 84, 598, 4199, 29409, 205882, 1441196, 10088397, 70618807, 494331680, 3460321794, 24222252595, 169555768205, 1186890377478, 8308232642392, 58157628496793, 407103399477603, 2849723796343276, 19948066574402990, 139636466020820991, 977455262145747001

Offset: 0

Vincenzo Librandi, Jul 09 2014

This formula is considered in Theorem 5 of Shum's paper in References: on page 4 reads M(7^m,3) = (7^m - 2*m - 1)/4 for m >= 1, where M(r,s) is the number of the codewords in an optimal CAC(r,s), and CAC(r,s) denotes a conflict-avoiding codes of length r and weight s (see Introduction).

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
K. W. Shum, On Conflict-Avoiding Codes of Weight Three and Odd Length, The Fifth International Workshop on Signal Design and Its Applications in Communications, October 10-14, 2011, Guilin, China.
Index entries for linear recurrences with constant coefficients, signature (9,-15,7).

Cf. A000420, A005408, A111277, A135304.

Magma
```
[(7^n-2*n-1)/4: n in [0..25]];
```

Table[(7^n - 2 n - 1)/4, {n, 0, 30}] (* or *)
CoefficientList[Series[x (1 + 2 x)/((1 - 7 x) (1 - x)^2), {x, 0, 30}], x]

G.f.: x*(1+2*x)/((1-7*x)*(1-x)^2).
a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). - Robert Israel, Jul 09 2014
From Elmo R. Oliveira, Apr 02 2025: (Start)
E.g.f.: exp(x)*(exp(6*x) - (2*x + 1))/4.
a(n) = (A000420(n) - A005408(n))/4. (End)

Edited by Bruno Berselli, Jul 09 2014

cp's OEIS Frontend

A244975 a(n) = (7^n - 2*n - 1)/4.

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