login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072229 Witt index of the standard bilinear form <1,1,1,...,1> over the 2-adic rationals. 1
0, 0, 0, 0, 1, 2, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 9, 10, 11, 12, 12, 12, 12, 13, 14, 15, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20, 21, 22, 23, 24, 24, 24, 24, 25, 26, 27, 28, 28, 28, 28, 29, 30, 31, 32, 32, 32, 32, 33, 34, 35, 36, 36, 36, 36, 37, 38, 39, 40, 40, 40, 40, 41, 42 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

There is another interesting bilinear form over Q_2 : it is <1, ..., 1, 2>. It has Witt index 0, 0, 0, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 7, 7, ...

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 1, -1).

FORMULA

a(n) = 4 floor(n/7) + [0,0,0,0,1,2,3][n%7 + 1]. [Formula corrected by Franklin T. Adams-Watters, Apr 13 2009]

From R. J. Mathar, Apr 16 2009: (Start)

a(n) = a(n-1) + a(n-7) - a(n-8).

G.f.: x^4*(1+x)*(1+x^2)/((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2). (End)

MAPLE

for n from 0 to 120 do printf("%d, ", 4*floor(n/7)+op( (n mod 7)+1, [0, 0, 0, 0, 1, 2, 3]) ) ; od: # R. J. Mathar, Apr 16 2009

MATHEMATICA

LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 0, 0, 0, 1, 2, 3, 4}, 80] (* Harvey P. Dale, Jun 21 2012 *)

PROG

(Haskell)

a072229 n = a072229_list !! n

a072229_list = [0, 0, 0, 0, 1, 2, 3, 4] ++ zipWith (+)

               (zipWith (-) (tail a072229_list) a072229_list)

               (drop 7 a072229_list)

-- Reinhard Zumkeller, Nov 02 2015

(PARI) a(n)=n\7*4 + [0, 0, 0, 0, 1, 2, 3][n%7 + 1] \\ Charles R Greathouse IV, Feb 09 2017

CROSSREFS

Sequence in context: A140427 A194816 A178770 * A120509 A029106 A064004

Adjacent sequences:  A072226 A072227 A072228 * A072230 A072231 A072232

KEYWORD

nonn,nice,easy

AUTHOR

Gaël Collinet, Jul 05 2002

EXTENSIONS

More terms from R. J. Mathar, Apr 16 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified November 20 00:42 EST 2017. Contains 294957 sequences.