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%I #33 Jan 30 2024 20:19:55
%S 1,2,2,4,4,6,6,8,8,10,10,12,12,14,14,16,16,18,18,20,20,22,22,24,24,26,
%T 26,28,28,30,30,32,32,34,34,36,36,38,38,40,40,42,42,44,44,46,46,48,48,
%U 50,50,52,52,54,54,56,56,58,58,60,60,62,62,64,64,66,66,68,68,70,70,72
%N 1 followed by repeats of 2*k.
%H Stefano Spezia, <a href="/A131055/b131055.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F Inverse binomial transform of A131056: (1, 3, 7, 17, 41, 97, 225, ...).
%F From _Colin Barker_, Oct 28 2012: (Start)
%F a(n) = ((-1)^n + 2*n-1)/2 for n > 1.
%F a(n) = a(n-1) + a(n-2) - a(n-3) for n > 1.
%F G.f.: x*(x^3-x^2+x+1)/((x-1)^2*(x+1)). (End)
%F E.g.f.: x*(exp(x) + 1) - sinh(x). - _Stefano Spezia_, Jan 28 2024
%p seq(`if`(n=1, 1, n-(n mod 2)), n=1..72);
%t Join[{1}, Table[2*Floor[i/2], {i, 2, 81}]] (* _Stefan Steinerberger_, Jun 13 2007 *)
%t With[{c=2*Range[40]},Join[{1},Riffle[c,c]]] (* _Harvey P. Dale_, Jul 25 2019 *)
%Y Cf. A131056.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Jun 12 2007
%E More terms from _Stefan Steinerberger_, Jun 13 2007
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