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 A226377 #9 Jul 31 2013 22:24:16 %S A226377 1,3,2,4,1,-1,7,3,2,3,11,4,1,-1,-4,18,7,3,2,3,7,29,11,4,1,-1,-4,-11, %T A226377 47,18,7,3,2,3,7,18,76,29,11,4,1,-1,-4,-11,-29,123,47,18,7,3,2,3,7,18, %U A226377 47,199,76,29,11,4,1,-1,-4,-1,-29,-76,-199 %N A226377 Lucas numbers differences triangle T(n,k), k<=n, where column k+1 holds the k-th differences of A000204, read by rows. %C A226377 Consecutive columns (i.e. k =1,2,3...) shift the Lucas sequence (A000204) down by 2 indices. %C A226377 Diagonal (n=k) produces A061084, and Lucas numbers at increasingly negative indices for n=k>2. %C A226377 Row sums equal A203976(n) for n=>1, which equals Lucas numbers A000204(n) if n is odd, and 5 * A000045(2*n) (Fibonacci) if n is even. %C A226377 Compare A227431 which is a differences triangle for the Fibonacci sequence A000045. %F A226377 T(n,1) = A000204(n) for n>0, T(n,k) = T(n,k-1) - T(n-1,k-1). %e A226377 Triangle begins: %e A226377 1; %e A226377 3, 2; %e A226377 4, 1, -1; %e A226377 7, 3, 2, 3; %e A226377 11, 4, 1, -1, -4; %e A226377 18, 7, 3, 2, 3, 7; %e A226377 29, 11, 4, 1, -1, -4, -11; %e A226377 47, 18, 7, 3, 2, 3, 7, 18; %e A226377 76, 29, 11, 4, 1, -1, -4, -11, -29; %e A226377 ... %Y A226377 Cf. A000204, A203976 %K A226377 sign,tabl %O A226377 1,2 %A A226377 _Richard R. Forberg_, Jul 31 2013