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, 93825009014101, 375300002501973, 1501199942899029

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

From Elmo R. Oliveira, Nov 13 2025: (Start)

E.g.f.: exp(x)*(exp(3*x) + 3*exp(x) - 1)/3.

a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3). (End)

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)
(Python) A079319=lambda n: 2**n + 4**n//3 # M. F. Hasler, May 28 2024

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