A242179 T(0,0) = 1, T(n+1,2*k) = - T(n,k), T(n+1,2*k+1) = T(n,k), k=0..n, triangle read by rows.

1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1

Offset

0

Comments

Row n has 2^n terms;

sum of row n = 0 for n > 0, cf. A000007;

numerator of Bernoulli tree, see Woon link; denominators = A106831.

Links

Reinhard Zumkeller, Rows n = 0..12 of table, flattened

S. C. Woon, A tree for generating Bernoulli numbers, Math. Mag., 70 (1997), 51-56.

Index entries for sequences related to Bernoulli Numbers.

Prog

(Haskell)
a242179  n k = a242179_tabf !! n !! n
a242179_row n = a242179_tabf !! n
a242179_tabf = iterate (concatMap (\x -> [-x, x])) [1] :: (Num t => [[t]])
a242179_list = concat a242179_tabf
(PARI) T(n, k) = (-1)^(n - hammingweight(k));
a(n) = n++; -(-1)^(logint(n, 2) - hammingweight(n)); \\ Kevin Ryde, Mar 11 2021

Crossrefs

Cf. A059448 (values 0,1), A298952 (values 1,0).

Cf. A106831, A060054, A075180, A164555, A027642.

Sequence in context: A070748 A154990 A209615 * A319117 A063747 A210245

Adjacent sequences: A242176 A242177 A242178 * A242180 A242181 A242182

Keyword

sign,tabf,frac

Author

Reinhard Zumkeller, Jul 04 2014

Status

approved