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.

0, 1, 1, 2, 3, 5, 8, 114, 15476, 241627833, 58387782699138722, 3409133182630874269408219655206824, 11622189056914914134468868887744166891725722891927072453845737486189

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..12.

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

Adjacent sequences: A120492 A120493 A120494 * A120496 A120497 A120498

Keyword

nonn,uned

Author

Roger L. Bagula, Aug 06 2006

Status

approved