A120496 A determinant sum sequence of the D3 dihehral 2 X 2 representation.

0, 1, 1, 2, 3, 5, 8, 0, 126, 15124, 228599471, 52257714939029891, 2730868770648907374112617772230042, 7457644242505474665594789454437375968542531762348793682274118549669

Offset

0,4

Links

Table of n, a(n) for n=0..13.

Formula

a0 = 1/2; b0 = Sqrt[3]/2; s[6] = IdentityMatrix[2]; s[1] = {{-a0, -b0}, {b, -a0}}; s[2] = {{-a0, b0}, {-b0, -a0}}; s[4] = {{1, 0}, {0, -1}}; s[3] = {{a0, b0}, {b0, -a0}}; s[5] = {{a0, -b0}, {-b0, -a0}}; 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

(*http : // mathworld.wolfram.com/DihedralGroupD3.html*) a0 = 1/2; b0 = Sqrt[3]/2; s[6] = IdentityMatrix[2]; s[1] = {{-a0, -b0}, {b, -a0}}; s[2] = {{-a0, b0}, {-b0, -a0}}; s[4] = {{1, 0}, {0, -1}}; s[3] = {{a0, b0}, {b0, -a0}}; s[5] = {{a0, -b0}, {-b0, -a0}}; 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: A145380 A136740 A105994 * A105150 A008963 A031324

Adjacent sequences: A120493 A120494 A120495 * A120497 A120498 A120499

Keyword

nonn,uned

Author

Roger L. Bagula, Aug 06 2006

Status

approved