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A120494
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A vector group determinant sequence in which the next element is made by a sum of the older elements over a vector like 2 X 2 matrix group.
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0
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1, 1, 2, 3, 5, 13, 139, 19136, 366167031, 134078294225149313, 17976988982325707481237962186849833, 323172132870659875927245721269598505772051876540063951439000722587455
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This sequence type gets very large very fast.
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FORMULA
| s[1] = {{1, 0}, {0, 1}}; s[2] = {{1, 0}, {0, -1}}; s[3] = {{0, 1}, {1, 0}}; s[4] = {{0, 1}, {-1, 0}}; a[0] = {0, 1, 1, 2}; a[1] = {1, 1, 2, 3}; a[n_] := a[n] = {a[n - 1][[2]], a[n - 1][[3]], a[n - 1][[4]], Det[Sum[a[n - 1][[i]]*s[i], {i, 1, 4}]]} a(n)=a[n][[1]]
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MATHEMATICA
| s[1] = {{1, 0}, {0, 1}}; s[2] = {{1, 0}, {0, -1}}; s[3] = {{0, 1}, {1, 0}}; s[4] = {{0, 1}, {-1, 0}}; a[0] = {0, 1, 1, 2}; a[1] = {1, 1, 2, 3}; a[n_] := a[n] = {a[n - 1][[2]], a[n - 1][[3]], a[n - 1][[4]], Det[Sum[a[n - 1][[i]]*s[i], {i, 1, 4}]]} Table[a[n][[1]], {n, 1, 15}]
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CROSSREFS
| Sequence in context: A005478 A117740 A041047 * A164825 A038601 A114747
Adjacent sequences: A120491 A120492 A120493 * A120495 A120496 A120497
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Aug 06 2006
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