A317188 a(n) = 1 + 2 * (a(n-1) + a(n-4) + a(n-6)) + a(n-7) for n>3, with initial values 0 if n<0, and 1,3,8,18 for n=0..3.

1, 3, 8, 18, 39, 85, 189, 422, 942, 2099, 4673, 10400, 23148, 51528, 114709, 255359, 568460, 1265450, 2817015, 6270953, 13959773, 31075874, 69178058, 153997383, 342813793, 763138256, 1698823128, 3781752544, 8418564665, 18740578667, 41718428560, 92869452514

Offset: 0

Author

Tomas Rokicki, Jul 28 2018

Keywords

• nonn
• easy

Comments

Some mail programs automatically include copies of all earlier messages in the same thread. In some cases (especially when rich text format is used) any unrecognized character is replaced by two copies of itself, leading to exponential growth.

The present sequence illustrates this growth for UTF-8 encoding and the CP1252 character set, for the single code point 150.

References

• Fred Lunnon and Tomas Rokicki, Posting to Math Fun Mailing List, circa Jul 25 2018

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,0,2,-2,2,-1,-1).

Programs

Mathematica

LinearRecurrence[{3,-2,0,2,-2,2,-1,-1},{1,3,8,18,39,85,189,422},40] (* Harvey P. Dale, Oct 15 2021 *)

Formula

G.f.: -(x^4-x^2-1)/((x-1)*(x+1)*(x^6+x^5-x^4+3*x^3-3*x^2+3*x-1)). - Alois P. Heinz, Jul 28 2018

Extensions

More terms from Altug Alkan, Jul 28 2018