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 A047862 #30 Sep 08 2022 08:44:57 %S A047862 1,7,20,48,108,236,508,1084,2300,4860,10236,21500,45052,94204,196604, %T A047862 409596,851964,1769468,3670012,7602172,15728636,32505852,67108860, %U A047862 138412028,285212668,587202556,1207959548,2483027964,5100273660,10468982780,21474836476 %N A047862 a(n) = T(5,n), array T given by A047858. %C A047862 n-th difference of a(n), a(n-1), ..., a(0) is (6, 7, 8, ...). %C A047862 More generally the main diagonal of the array defined by T(0,j) = j+1 with j>=0, T(i,0) = i+1 with i>=0, T(i,j) = T(i-1,j-1) + T(i-1,j) + A, is given by T(n,n) = 2^(n-1)*(n+2*A+2)-A. - _Benoit Cloitre_, Jun 17 2003 %H A047862 Vincenzo Librandi, <a href="/A047862/b047862.txt">Table of n, a(n) for n = 0..3000</a> %H A047862 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4). %F A047862 From _Benoit Cloitre_, Jun 17 2003: (Start) %F A047862 Main diagonal of the array defined by T(0, j) = j+1 with j>=0, T(i, 0) = i+1 with i>=0, T(i,j) = T(i-1,j-1)+T(i-1,j)+ 4. Therefore, for i = j = n: %F A047862 a(n) = 2^(n-1)*(n+10)-4. (End) %F A047862 a(0)=1, a(1)=7, a(2)=20; for n>2, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - _Vincenzo Librandi_, Sep 28 2011 %F A047862 a(n) = 2^(n-1)*(n+10)-4. G.f.: (1+2*x-7*x^2) / ((1-x)*(1-2*x)^2). - _Colin Barker_, Feb 18 2016 %o A047862 (Magma) [2^(n-1)*(n+10)-4: n in [0..30]]; // _Vincenzo Librandi_, Sep 28 2011 %o A047862 (PARI) Vec((1+2*x-7*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ _Colin Barker_, Feb 18 2016 %K A047862 nonn,easy %O A047862 0,2 %A A047862 _Clark Kimberling_