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A139792 First quadrisection of A139763 (1, 2, 3, 4, 11, ...).

%I A139792 #33 Feb 27 2024 03:05:25
%S A139792 1,11,171,2731,43691,699051,11184811,178956971,2863311531,45812984491,
%T A139792 733007751851,11728124029611,187649984473771,3002399751580331,
%U A139792 48038396025285291,768614336404564651,12297829382473034411,196765270119568550571,3148244321913096809131
%N A139792 First quadrisection of A139763 (1, 2, 3, 4, 11, ...).
%H A139792 Vincenzo Librandi, <a href="/A139792/b139792.txt">Table of n, a(n) for n = 0..500</a>
%H A139792 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16)
%F A139792 a(n) = 16*a(n-1) - 5.
%F A139792 a(n) = 10*A131865(n) + 1.
%F A139792 G.f.: ( 1-6*x ) / ( (16*x-1)*(x-1) ). - _R. J. Mathar_, Feb 06 2011
%F A139792 E.g.f.: (exp(x) + 2*exp(16*x))/3. - _G. C. Greubel_, Nov 03 2018
%F A139792 From _Jianing Song_, Aug 30 2022: (Start)
%F A139792 a(n) = A001045(4*n+1).
%F A139792 a(n+1) - a(n) = 10*A001025(n). (End)
%t A139792 Table[(1 + 2^(4*n+1))/3, {n,0,20}] (* _G. C. Greubel_, Nov 03 2018 *)
%o A139792 (Magma) [(1+2*16^n)/3: n in [0..20]]; // _Vincenzo Librandi_, Aug 09 2011
%o A139792 (PARI) vector(20, n, n--; (1 + 2^(4*n+1))/3) \\ _G. C. Greubel_, Nov 03 2018
%Y A139792 Second quadrisection of Jacobsthal numbers A001045; the other quadrisections are A195156 (first), A144864 (third), and A141060 (fourth).
%K A139792 nonn,easy
%O A139792 0,2
%A A139792 _Paul Curtz_, May 21 2008