cp's OEIS Frontend

A133124 A007318 * [1, 2, 2, 3, 2, 3, 2, 3, 2, ...].

%I A133124 #18 Jun 08 2025 02:48:16
%S A133124 1,3,7,16,35,74,153,312,631,1270,2549,5108,10227,20466,40945,81904,
%T A133124 163823,327662,655341,1310700,2621419,5242858,10485737,20971496,
%U A133124 41943015,83886054,167772133,335544292,671088611,1342177250,2684354529,5368709088,10737418207,21474836446
%N A133124 A007318 * [1, 2, 2, 3, 2, 3, 2, 3, 2, ...].
%H A133124 G. C. Greubel, <a href="/A133124/b133124.txt">Table of n, a(n) for n = 0..1000</a>
%H A133124 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A133124 Binomial transform of [1, 2, 2, 3, 2, 3, 2, 3, 2, ...].
%F A133124 a(n) = 5*2^(n-1) - (n+1), for n >= 1.
%F A133124 Row sums of triangle A133938. - _Gary W. Adamson_, Sep 29 2007
%F A133124 G.f.: 1 + x*(3-5*x+3*x^2)/((1-2*x)*(1-x)^2). - _R. J. Mathar_, Nov 14 2007
%F A133124 E.g.f.: (5*exp(2*x) - 2*(1+x)*exp(x) - 1)/2. - _G. C. Greubel_, Oct 21 2017
%e A133124 a(3) = (1, 3, 3, 1) dot (1, 2, 2, 3) = (1 + 6 + 6 + 3).
%e A133124 a(5) = 74 = 2^6 + 2^4 - 6 = 64 + 16 - 6.
%t A133124 Join[{1}, Table[5*2^(n-1) - n -1, {n,1,50}]] (* _G. C. Greubel_, Oct 21 2017 *)
%t A133124 LinearRecurrence[{4,-5,2},{1,3,7,16},40] (* _Harvey P. Dale_, Jun 18 2024 *)
%o A133124 (PARI) concat(1, for(n=1,50, print1(5*2^(n - 1) - n - 1, ", "))) \\ _G. C. Greubel_, Oct 21 2017
%o A133124 (Magma) [1] cat [5*2^(n - 1) - n -1: n in [1..50]]; // _G. C. Greubel_, Oct 21 2017
%Y A133124 Cf. A000079, A133938.
%K A133124 nonn,easy
%O A133124 0,2
%A A133124 _Gary W. Adamson_, Sep 19 2007
%E A133124 Terms a(9) onward added by _G. C. Greubel_, Oct 21 2017