0,3

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for linear recurrences with constant coefficients, signature (0,19,0,-50,0,32).

From Colin Barker, Dec 30 2015 and Apr 16 2019: (Start)

a(n) = 19*a(n-2)-50*a(n-4)+32*a(n-6) for n>9.

G.f.: (1+x-9*x^2+48*x^3-24*x^4+448*x^5-1504*x^6+3584*x^7+1536*x^8-4096*x^9) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)). (End)

a(n) = (1 - (-1)^n)*(2*4^n - 1)/2 + ((1 + (-1)^n)*(94 + 29*2^(1/2))/4 - 47)*2^((n+1)/2) for n>3. Therefore: for even n>2, a(n) = 29*2^(n/2); for odd n>3, a(n) = 2^(2*n+1) - 47*2^((n+1)/2) - 1. [Bruno Berselli, Dec 30 2015]

rule=25; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)

(Python) print([1, 1, 10, 67] + [2*4**n-47*2**((n+1)//2)-1 if n%2 else 29*2**(n//2) for n in range(4, 30)]) # Karl V. Keller, Jr., Jul 05 2021

Cf. A266441.

Sequence in context: A377917 A231886 A278090 * A108275 A086443 A172066

Adjacent sequences: A266440 A266441 A266442 * A266444 A266445 A266446

nonn,easy

Robert Price, Dec 29 2015

approved