A120659 A determinant sum sequence of the D5 dihehral 2 X 2 representation.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 2483, 6053383, 36651957891448, 1343366154248994863013047386, 1804632624381764689171354018874685160689875147803208124

Offset

0,4

References

(*http : // mathworld.wolfram.com/DihedralGroupD3.html*)

Links

Table of n, a(n) for n=0..15.

Formula

<< MathWorld`Groups` M0 = DihedralGroupMatrices[5]; s[n_] := M0[[n]] a[0] = Table[Fibonacci[n], {n, 0, 9}]; a[1] = Table[Fibonacci[n], {n,1, 10}]; a[n_] := a[n] = {a[n - 1][[2]], a[n - 1][[3]], a[n - 1][[4]], a[n - 1][[5]], a[n - 1][[6]], a[n - 1][[7]], a[n - 1][[8]], a[n - 1][[9]], a[n - 1][[10]], Abs[Det[Sum[a[n - 1][[i]]*s[i], {i, 1, 10}]]]}

Mathematica

Clear[a, f, s] (*http : // mathworld.wolfram.com/DihedralGroupD3.html*) << MathWorld`Groups` M0 = DihedralGroupMatrices[5]; s[n_] := M0[[n]] a[0] = Table[Fibonacci[n], {n, 0, 9}]; a[1] = Table[Fibonacci[n], {n, 1, 10}]; a[n_] := a[n] = {a[n - 1][[2]], a[n - 1][[3]], a[n - 1][[4]], a[n - 1][[5]], a[n - 1][[6]], a[n - 1][[7]], a[n - 1][[8]], a[n - 1][[9]], a[n - 1][[10]], Abs[Det[Sum[a[n - 1][[i]]*s[i], {i, 1, 10}]]]} Table[Floor[a[n][[1]]], {n, 0, 16}]

Crossrefs

Cf. A120495, A120496.

Sequence in context: A147659 A005181 A177376 * A042581 A349843 A302019

Adjacent sequences: A120656 A120657 A120658 * A120660 A120661 A120662

Keyword

nonn,uned

Author

Roger L. Bagula, Aug 10 2006

Status

approved