A139792 - OEIS

%I #33 Feb 27 2024 03:05:25

%S 1,11,171,2731,43691,699051,11184811,178956971,2863311531,45812984491,

%T 733007751851,11728124029611,187649984473771,3002399751580331,

%U 48038396025285291,768614336404564651,12297829382473034411,196765270119568550571,3148244321913096809131

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

%H Vincenzo Librandi, <a href="/A139792/b139792.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16)

%F a(n) = 16*a(n-1) - 5.

%F a(n) = 10*A131865(n) + 1.

%F G.f.: ( 1-6*x ) / ( (16*x-1)*(x-1) ). - _R. J. Mathar_, Feb 06 2011

%F E.g.f.: (exp(x) + 2*exp(16*x))/3. - _G. C. Greubel_, Nov 03 2018

%F From _Jianing Song_, Aug 30 2022: (Start)

%F a(n) = A001045(4*n+1).

%F a(n+1) - a(n) = 10*A001025(n). (End)

%t Table[(1 + 2^(4*n+1))/3, {n,0,20}] (* _G. C. Greubel_, Nov 03 2018 *)

%o (Magma) [(1+2*16^n)/3: n in [0..20]]; // _Vincenzo Librandi_, Aug 09 2011

%o (PARI) vector(20, n, n--; (1 + 2^(4*n+1))/3) \\ _G. C. Greubel_, Nov 03 2018

%Y Second quadrisection of Jacobsthal numbers A001045; the other quadrisections are A195156 (first), A144864 (third), and A141060 (fourth).

%K nonn,easy

%O 0,2

%A _Paul Curtz_, May 21 2008