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A122958 a(0)=1, a(n) = 2 - 2^(n-1) for n>0.

%I A122958 #36 May 30 2024 00:31:08
%S A122958 1,1,0,-2,-6,-14,-30,-62,-126,-254,-510,-1022,-2046,-4094,-8190,
%T A122958 -16382,-32766,-65534,-131070,-262142,-524286,-1048574,-2097150,
%U A122958 -4194302,-8388606,-16777214,-33554430,-67108862,-134217726,-268435454,-536870910,-1073741822,-2147483646
%N A122958 a(0)=1, a(n) = 2 - 2^(n-1) for n>0.
%C A122958 Take square of A014217 (1,1,2,4,6) and successive differences: a(n) is principal diagonal (k-th term of k-th row). a(n) differences: 0, -1, -2, -4, -8, -16, ... = -A131577. - _Paul Curtz_, Sep 26 2008
%H A122958 Vincenzo Librandi, <a href="/A122958/b122958.txt">Table of n, a(n) for n = 0..1000</a>
%H A122958 Yasemin Alp and E. Gokcen Kocer, <a href="https://doi.org/10.1007/s00025-024-02193-5">Exponential Almost-Riordan Arrays</a>, Results Math. (2024) Vol. 79, 173.
%H A122958 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A122958 a(0) = 1, a(1) = 1, a(2) = 0, a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
%F A122958 G.f.: (1 - 2*x - x^2)/(1 - 3*x + 2*x^2).
%F A122958 a(n) = -A000918(n-1) for n>0.
%F A122958 a(n+1) = 2*a(n) - 2 for n>0. - _Michael Somos_, Feb 08 2015
%F A122958 E.g.f.: exp(x)*(2 - cosh(x)). - _Stefano Spezia_, May 07 2023
%e A122958 G.f. = 1 + x - 2*x^3 - 6*x^4 - 14*x^5 - 30*x^6 - 62*x^7 - 126*x^8 - 254*x^9 + ...
%t A122958 Join[{1}, LinearRecurrence[{3, -2}, {1, 0}, 50]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 24 2012 *)
%t A122958 Join[{1},2-2^#&/@Range[0,30]] (* _Harvey P. Dale_, Jan 19 2021 *)
%o A122958 (PARI) {a(n) = if( n<1, n==0, 2 - 2^(n-1))}; /* _Michael Somos_, Feb 08 2015 */
%Y A122958 Apart from signs, same as A000918.
%Y A122958 Cf. A131577.
%K A122958 sign,easy
%O A122958 0,4
%A A122958 _Philippe Deléham_, Oct 26 2006
%E A122958 Corrected a(22) by _Vincenzo Librandi_, Aug 11 2011