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 A131328 #15 Jul 12 2017 16:36:10 %S A131328 1,4,5,12,17,32,49,84,133,220,353,576,929,1508,2437,3948,6385,10336, %T A131328 16721,27060,43781,70844,114625,185472,300097,485572,785669,1271244, %U A131328 2056913,3328160,5385073,8713236,14098309,22811548,36909857,59721408,96631265,156352676 %N A131328 Row sums of triangle A131327. %C A131328 a(n)/a(n-1) tends to phi. (Cf. A062114). %H A131328 Colin Barker, <a href="/A131328/b131328.txt">Table of n, a(n) for n = 0..1000</a> %H A131328 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-1). %F A131328 a(n+1) = A131326(n) + A052952(n+1). %F A131328 a(n) = -3*(1+(-1)^n)/2 +4*A000045(n+1). - _R. J. Mathar_, Aug 13 2012 %F A131328 G.f.: ( 1+3*x-x^2 ) / ( (x-1)*(1+x)*(x^2+x-1) ). - _R. J. Mathar_, Aug 13 2012 %F A131328 From _Colin Barker_, Jul 12 2017: (Start) %F A131328 a(n) = (2^(1-n)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) - 3 for n even. %F A131328 a(n) = (2^(1-n)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) for n odd. %F A131328 a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3. %F A131328 (End) %e A131328 a(3) = 12 = sum of row 3 terms of A131327: (3 + 5 + 3 + 1). %e A131328 a(3) = (9 + 3) since we add terms of A131326: (1, 3, 4, 9, 13,...) to A052952: (0, 1, 1, 3, 4,...), getting (9 + 3 ) = 12. %o A131328 (PARI) Vec((1 + 3*x - x^2) / ((1 - x)*(1 + x)*(1 - x - x^2)) + O(x^50)) \\ _Colin Barker_, Jul 12 2017 %Y A131328 Cf. A062114, A052952, A131324, A131325, A131326, A131327. %K A131328 nonn,easy %O A131328 0,2 %A A131328 _Gary W. Adamson_, Jun 28 2007 %E A131328 More terms from _Colin Barker_, Jul 12 2017