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A244961 Decimal equivalent of the binary string generated by the n X n antidiagonal matrix read by rows. 1
1, 6, 84, 4680, 1118480, 1108378656, 4467856773184, 72624976668147840, 4740885567116192841984, 1240362622532514091484054016, 1299343104384081987198247370753024, 5447177625434934817180194985991294945280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The binary representation of a(n), padded with zeros on the left to make an n^2-bit binary number, where the digits are grouped into n rows of n digits, form an n X n binary matrix whose entries along the antidiagonal are 1's and 0's everywhere else. a(n) will be the smallest integer whose binary representation forms an n X n involutory matrix. (I.e., let M be the n X n matrix formed by this binary representation of a(n); then a(n) is the smallest integer such that M^2 = I_n (the n X n unit matrix).)

LINKS

Nathan J. Russell, Table of n, a(n) for n = 1..30

FORMULA

a(n) = Sum_{k=1..n} 2^((n-1)k).

a(1) = 1, a(n) = (2^(n^2)-2^n)/(2^n-2) when n>1.

EXAMPLE

n=1 -> a(1) = 1 -> M = {{1}} -> M^2 = I_1 = 1.

n=2 -> a(2) = 6 = 0110_2 -> M ={{0, 1}, {1, 0}} -> M^2 = I_2.

n=3 -> a(3) = 84 = 001010100_2 -> M ={{0, 0, 1}, {0, 1, 0}, {1, 0, 0}}.

MATHEMATICA

For[b = 2, b <= 10, ++b, Print[(2^b^2 - 2^b)/(2^b - 2)]; ]

PROG

(PARI) a(n) = if (n==1, 1, (2^(n^2)-2^n)/(2^n-2)); \\ Michel Marcus, Jul 11 2014

(Magma) [1] cat[(2^(n^2)-2^n)/(2^n-2): n in [2..15]]; // Vincenzo Librandi, Jul 26 2014

CROSSREFS

Sequence in context: A171200 A195245 A030031 * A293455 A334516 A331014

Adjacent sequences: A244958 A244959 A244960 * A244962 A244963 A244964

KEYWORD

nonn,base

AUTHOR

Nathan J. Russell, Jul 08 2014

EXTENSIONS

Edited by Wolfdieter Lang, Jul 25 2014

STATUS

approved

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Last modified January 29 13:51 EST 2023. Contains 359923 sequences. (Running on oeis4.)