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

Author

Adam P. Goucher, Apr 20 2015

Keywords

• nonn
• easy

Examples

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

Links

• LifeWiki, Sawtooth 201
• Index entries for linear recurrences with constant coefficients, signature (48,-47).

Crossrefs

Cf. A218750.

Programs

Mathematica

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

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