A120495 - OEIS

%I #4 Mar 12 2014 16:36:53

%S 0,1,1,2,3,5,8,114,15476,241627833,58387782699138722,

%T 3409133182630874269408219655206824,

%U 11622189056914914134468868887744166891725722891927072453845737486189

%N A vector group determinant sequence in which the next element is made by a sum of the older elements over a six element sl(2,2) vector like 2 X 2 matrix group.

%C An absolute value was used in the determinant step to keep the result positive.

%F s[1] = {{1, 0}, {0, 1}}; s[2] = {{0, 1}, {1, 1}}; s[3] = {{1, 1}, {1, 0}}; s[4] = {{1, 0}, {1, 1}}; s[5] = {{1, 1}, {0, 1}}; s[6] = {{0, 1}, {1, 0}}; a[0] = {0, 1, 1, 2, 3, 5}; a[1] = {1, 1, 2, 3, 5, 8}; a[n_] := a[n] = {a[n - 1][[2]], a[n - 1][[3]], a[n - 1][[4]], a[n - 1][[5]], a[n - 1][[6]], Abs[ Det[Sum[a[n - 1][[i]]*s[i], {i, 1, 6}]]]} a(n)=a[n][[1]]

%t s[1] = {{1, 0}, {0, 1}}; s[2] = {{0, 1}, {1, 1}}; s[3] = {{1, 1}, {1, 0}}; s[4] = {{1, 0}, {1, 1}}; s[5] = {{1, 1}, {0, 1}}; s[6] = {{0, 1}, {1, 0}}; a[0] = {0, 1, 1, 2, 3, 5}; a[1] = {1, 1, 2, 3, 5, 8}; a[n_] := a[n] = {a[n - 1][[2]], a[n - 1][[3]], a[n - 1][[4]], a[n - 1][[5]], a[n - 1][[6]], Abs[ Det[Sum[a[n - 1][[i]]*s[i], {i, 1, 6}]]]} Table[a[n][[1]], {n, 0, 15}]

%K nonn,uned

%O 0,4

%A _Roger L. Bagula_, Aug 06 2006