A079319 a(0) = 1; for n >= 1, a(n) = 4*a(n-1) - (2^n-1).

1, 3, 9, 29, 101, 373, 1429, 5589, 22101, 87893, 350549, 1400149, 5596501, 22377813, 89494869, 357946709, 1431721301, 5726754133, 22906754389, 91626493269, 366504924501, 1466017600853, 5864066209109, 23456256447829

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

David Singmaster, On the cellular automaton of Ulam and Warburton, M500 Magazine of the Open University, #195 (December 2003), pp. 2-7. Also cached copy, included with permission.

Index entries for linear recurrences with constant coefficients, signature (7, -14, 8).

Formula

a(n) = 2^n + (4^n-1)/3, n>=0.

a(n) = Sum_{i = 0..2^n - 1} A079314(i).

G.f.: (1-4x+2x^2)/((1-x)(1-2x)(1-4x)).

Mathematica

A079319list[nmax_]:=LinearRecurrence[{7, -14, 8}, {1, 3, 9}, nmax+1]; A079319list[50] (* Paolo Xausa, Jul 30 2023 *)

Prog

(PARI) a(n)=if(n<0, 0, 2^n+(4^n-1)/3)

Crossrefs

Cf. A079314, A079315, A079316, A079317, A079318.

Records in A085194.

Sequence in context: A275014 A278404 A148941 * A112532 A148942 A109432

Adjacent sequences: A079316 A079317 A079318 * A079320 A079321 A079322

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 12 2003

Status

approved