|
|
A119408
|
|
Decimal equivalent of the binary string generated by the n X n identity matrix.
|
|
3
|
|
|
1, 9, 273, 33825, 17043521, 34630287489, 282578800148737, 9241421688590303745, 1210107565283851686118401, 634134936313486520338360567809, 1329552593586084350528447794605199361, 11151733894906779683522195341810241573494785
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) is divisible by 2^n - 1. a(n) == n mod 2^(n+1) - 1. - Robert Israel, Jun 09 2015
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2^((n+1)(n-1)) + 2^((n+1)(n-2)) + ... + 1 where n=2,3,...
a(n) = (2^n*2^(n^2)-1)/(2*2^n-1). - Stuart Bruff, Jun 08 2015
|
|
EXAMPLE
|
n=2: [1 0; 0 1] == 1001_2 = 9;
n=3: [1 0 0; 0 1 0; 0 0 1] == 100010001_2 = 273;
n=4: [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1] == 1000010000100001_2 = 33825.
|
|
MATHEMATICA
|
For[n=2, n<=10, Print[n, " ", Sum[2^((n+1)(k-1)), {k, 1, n}]]; n++ ]
Table[FromDigits[Flatten[IdentityMatrix[n]], 2], {n, 15}] (* Harvey P. Dale, Dec 31 2021 *)
|
|
PROG
|
(MATLAB) for n = 1:10 bi2de((reshape(eye(n), length(eye(n))^2, 1))') end
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|