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
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).
Programs
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Mathematica
A079319list[nmax_]:=LinearRecurrence[{7,-14,8},{1,3,9},nmax+1];A079319list[50] (* Paolo Xausa, Jul 30 2023 *)
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PARI
a(n)=if(n<0,0,2^n+(4^n-1)/3)
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Python
A079319=lambda n: 2**n + 4**n//3 # M. F. Hasler, May 28 2024
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)).