A257319 Numbers n such that the n-th generation of Sawtooth 201 has minimum population in Conway's Game of Life.

0, 1840, 88320, 4152880, 195187200, 9173800240, 431168613120, 20264924818480, 952451466470400, 44765218924110640, 2103965289433201920, 98886368603360492080, 4647659324357943129600, 218439988244823327093040, 10266679447506696373374720

Offset

1,2

Links

Table of n, a(n) for n=1..15.

LifeWiki, Sawtooth 201

Index entries for linear recurrences with constant coefficients, signature (48,-47).

Formula

a(n) = 47*a(n-1) + 1840.

a(n) = (47^(n-1) - 1)*40. - Bill Gosper, Apr 25 2015

G.f.: 1840*x^2/((47*x-1)*(x-1)). - Alois P. Heinz, May 03 2015

E.g.f.: 40*(exp(47*x) - 47*exp(x) + 46)/47. - Stefano Spezia, Jul 04 2022

a(n) = 1840 * A218750(n-1). - Alois P. Heinz, Jul 04 2022

Example

The pattern begins at its minimum population of 201 at generation 0, and first returns to this population at generation 1840.

Mathematica

NestList[(47 # + 1840) &, 0, 100]
LinearRecurrence[{48, -47}, {0, 1840}, 20](* Harvey P. Dale, Sep 19 2017 *)

Crossrefs

Cf. A218750.

Sequence in context: A238294 A274683 A231079 * A287172 A243482 A252214

Adjacent sequences: A257316 A257317 A257318 * A257320 A257321 A257322

Keyword

nonn,easy

Author

Adam P. Goucher, Apr 20 2015

Status

approved