# [seqfan] Re: %F A100638 (?!)

Maximilian Hasler maximilian.hasler at gmail.com
Mon Dec 1 13:33:37 CET 2008

```On Mon, Dec 1, 2008 at 1:35 AM,  <franktaw at netscape.net> wrote:
> The "formula" line (beginning "Consider the matrix") is a bit confused,
> (...)  In other words, A=[a(1),a(2);a(3),a(4)],
> A^2=[a(5),a(6);a(7),a(8)], etc.

In fact this is not a formula but rather an example.
In "formula" should go the explicit expression of the n-th element.

> At a more basic level, how common is the notation [1,2;3,4] to
> represent the matrix:
> (1 2)
> (3 4)?
> PARI uses it, but I don't know whether it's in more general use.

MATLAB uses a similar notation with just spaces to separate elements:

>> A = [ 1 2 3; 3 4 5; 6 7 8]

I submitted the modified version below.
Maximilian

%S A100638 1,2,3,4,7,10,15,22,37,54,81,118,199,290,435,634,1069,1558,2337,3406,
%T A100638 5743,8370,12555,18298,30853,44966,67449,98302,165751,241570,362355,
%U A100638 528106,890461,1297782,1946673,2837134,4783807,6972050,10458075
! %N A100638 Elements of successive powers of the matrix A=[1,2;3,4].
! %F A100638 a(4n-3) = A124610(n), a(4n-2) = 2 A015535(n), a(4n-1) = 3
A015535(n), a(4n) = a(4n-3) + a(4n-1). - M. F. Hasler, Dec 01 2008
! %e A100638 Consider the matrix A=[1, 2; 3, 4]. Then a(1)=A_11,
a(2)=A_12, a(3)=A_21, a(4)=A_22,
! %e A100638 a(5)=(A^2)_11, a(6)=(A^2)_12, a(7)=(A^2)_21,
a(8)=(A^2)_22, a(9)=(A^3)_11, a(10)=(A^3)_12, ...
! %o A100638 A100638(n)=([1,2;3,4]^((n-1)\4+1))[(n-1)%4\2+1,2-n%2] /*
M. F. Hasler, Dec 01 2008 */
%Y A100638 Sequence in context: A078159 A129490 A018132
this_sequence A033320 A013982 A051449
%Y A100638 Adjacent sequences: A100635 A100636 A100637 this_sequence
A100639 A100640 A100641
%K A100638 easy,nonn
%O A100638 1,2
! %A A100638 Simone Severini (ss54(AT)york.ac.uk), Dec 04 2004

```