login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122948 First row sum of the 5 X 5 matrix M^n, where M = {{0, -1, 0, 0, 0}, {-1, 1, -1, 0, 0}, {0, -1, 1, -1, 0}, {0, 0, -1, 1, -1}, {0, 0, 0, -1, 1}}, n>=0. 1
1, -1, 1, -1, 1, 0, 4, 10, 33, 93, 264, 729, 1999, 5437, 14726, 39757, 107118, 288201, 774672, 2080936, 5587388, 14997840, 40249449, 108001720, 289774494, 777430359, 2085660586, 5595162045, 15009725921, 40264911876, 108013136968, 289750079191, 777264097335, 2085030095791 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..33.

FORMULA

a(n)=4a(n-1)-2a(n-2)-5a(n-3)+2a(n-4)+a(n-5) (follows from the minimal polynomial of the matrix M).

G.f.:(2*x-1)*(x^2-3*x+1)/(-1+x^5+2*x^4-5*x^3-2*x^2+4*x). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009

EXAMPLE

a(5)=0 because first row of M^5 is {6,-15,15,-10,4}.

MAPLE

with(linalg): M[1]:=matrix(5, 5, [0, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 1]): for n from 2 to 33 do M[n]:=multiply(M[1], M[n-1]) od: 1, seq(add(M[n][1, j], j=1..5), n=1..33);

a[0]:=1: a[1]:=-1: a[2]:=1: a[3]:=-1: a[4]:=1: for n from 5 to 33 do a[n]:=4*a[n-1]-2*a[n-2]-5*a[n-3]+2*a[n-4]+a[n-5] od: seq(a[n], n=0..33);

MATHEMATICA

M = {{0, -1, 0, 0, 0}, {-1, 1, -1, 0, 0}, {0, -1, 1, -1, 0}, {0, 0, -1, 1, -1}, {0, 0, 0, -1, 1}}; v[1] = {1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]

CROSSREFS

Cf. A098493.

Sequence in context: A052372 A052373 A007716 * A317800 A149171 A149172

Adjacent sequences: A122945 A122946 A122947 * A122949 A122950 A122951

KEYWORD

sign

AUTHOR

Gary W. Adamson and Roger L. Bagula, Oct 24 2006

EXTENSIONS

Edited by N. J. A. Sloane, Nov 24 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 27 01:14 EST 2022. Contains 358362 sequences. (Running on oeis4.)