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 A054457 #11 May 07 2025 09:12:40 %S A054457 1,6,27,104,366,1212,3842,11784,35223,103122,296805,842160,2360780, %T A054457 6549240,18004980,49106992,132996957,357948894,957993823,2550977112, %U A054457 6761742234,17848312884,46932923478,122980461816 %N A054457 Pell numbers A000129(n+1) (without P(0)) convoluted twice with itself. %C A054457 a(n)= A054456(n+2,2) (third column of Pell convolution triangle). %H A054457 Milan Janjić, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Janjic/janjic33.html">Hessenberg Matrices and Integer Sequences</a>, J. Int. Seq. 13 (2010) # 10.7.8, section 3. %H A054457 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,-4,9,6,1) %F A054457 a(n) = ((10*n^2+39*n+32)*P(n+1)+(n+1)*(4*n+11)*P(n))/32, where P(n)=A000129(n). %F A054457 G.f.: 1/(1-2*x-x^2)^3. %F A054457 a(n) = F''(n+3, 2)/2, that is, 1/2 times the 2nd derivative of the (n+3)th Fibonacci polynomial evaluated at x=2. - _T. D. Noe_, Jan 19 2006 %Y A054457 Cf. A054456, A000129, A006645. %K A054457 easy,nonn %O A054457 0,2 %A A054457 _Wolfdieter Lang_, Apr 27 2000