

A072229


Witt index of the standard bilinear form <1,1,1,...,1> over the 2adic 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. AdamsWatters, Apr 13 2009]
From R. J. Mathar, Apr 16 2009: (Start)
a(n) = a(n1) + a(n7)  a(n8).
G.f.: x^4*(1+x)*(1+x^2)/((x^6+x^5+x^4+x^3+x^2+x+1)*(x1)^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



