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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

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Last modified May 25 01:01 EDT 2017. Contains 287008 sequences.