This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A048746 #29 Aug 10 2024 03:34:33
%S A048746 1,6,17,44,109,266,645,1560,3769,9102,21977,53060,128101,309266,
%T A048746 746637,1802544,4351729,10506006,25363745,61233500,147830749,
%U A048746 356895002,861620757,2080136520,5021893801,12123924126,29269742057,70663408244,170596558549,411856525346,994309609245
%N A048746 Partial sums of A048655.
%H A048746 Harvey P. Dale, <a href="/A048746/b048746.txt">Table of n, a(n) for n = 0..1000</a>
%H A048746 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-1).
%F A048746 a(n) = 2*a(n-1) + a(n-2) + 4; a(0)=1, a(1)=6.
%F A048746 a(n) = ((6 + 5*sqrt(2))*(1 + sqrt(2))^n + (6 - 5*sqrt(2))*(1 - sqrt(2))^n)/4 - 2. [Corrected by _Stefano Spezia_, May 26 2024]
%F A048746 From _Colin Barker_, Sep 19 2012: (Start)
%F A048746 a(n) = 3*a(n-1) - a(n-2) - a(n-3).
%F A048746 G.f.: (1+3*x)/((1-x)*(1-2*x-x^2)). (End)
%F A048746 a(n) = 2*Pell(n) + 3*Pell(n+1) - 2, where Pell = A000129. - _Vladimir Reshetnikov_, Sep 27 2016
%F A048746 E.g.f.: exp(x)*(6*cosh(sqrt(2)*x) + 5*sqrt(2)*sinh(sqrt(2)*x) - 4)/2. - _Stefano Spezia_, May 26 2024
%t A048746 Accumulate[LinearRecurrence[{2,1},{1,5},30]] (* _Harvey P. Dale_, May 23 2012 *)
%t A048746 LinearRecurrence[{3, -1, -1},{1, 6, 17},26] (* _Ray Chandler_, Aug 03 2015 *)
%t A048746 Table[2 Fibonacci[n, 2] + 3 Fibonacci[n + 1, 2] - 2, {n, 0, 10}] (* _Vladimir Reshetnikov_, Sep 27 2016 *)
%Y A048746 Cf. A000129, A048655.
%K A048746 easy,nonn
%O A048746 0,2
%A A048746 _Barry E. Williams_
%E A048746 Corrected and extended by _T. D. Noe_, Nov 07 2006