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 A131913 #18 Jul 24 2024 03:05:17 %S A131913 1,3,6,13,25,48,89,163,294,525,929,1632,2849,4947,8550,14717,25241, %T A131913 43152,73561,125075,212166,359133,606721,1023168,1722625,2895843, %U A131913 4861254,8149933,13646809,22825200,38136089,63653827,106146534,176849517,294401825,489706272 %N A131913 Product of the square matrix in A065941 and the column vector (1, 2, 3, ...)'. %H A131913 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2,-1). %F A131913 a(n) = A010049(n) + A001629(n+2) = A055244(n+1) + A001629(n-1). %F A131913 From _Philippe Deléham_, Dec 28 2013: (Start) %F A131913 G.f.: (1+x-x^2)/(1-x-x^2)^2. %F A131913 a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4), a(0)=1, a(1)=3, a(2)=6, a(3)=13. %F A131913 a(n) = a(n-1) + a(n-2) + 2*Fibonacci(n). (End) %e A131913 a(4) = 25 = (1, 1, 3, 2, 1) dot (1, 2, 3, 4, 5) = (1 + 2 + 9 + 8 + 5), where (1, 1, 3, 2, 1) = row 4 of triangle A065941. %e A131913 a(4) = 25 = A010049(4) + A001629(6) = 5 + 20. %e A131913 a(5) = 48 = A055244(6) + A001629(4) = 43 + 5. %Y A131913 Cf. A000045, A065941, A010049, A001629, A055244. %K A131913 nonn,easy %O A131913 0,2 %A A131913 _Gary W. Adamson_, Jul 27 2007