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A120495 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. 1
0, 1, 1, 2, 3, 5, 8, 114, 15476, 241627833, 58387782699138722, 3409133182630874269408219655206824, 11622189056914914134468868887744166891725722891927072453845737486189 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
An absolute value was used in the determinant step to keep the result positive.
LINKS
FORMULA
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]]
MATHEMATICA
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}]
CROSSREFS
Sequence in context: A042667 A279073 A279074 * A107477 A271525 A357101
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Aug 06 2006
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)