A193212 Triangle T(n, k): T(n, 1) = n, T(n, n) = -n if n>1, T(n, k+n) = T(n, k) if n>1.

1, 2, -2, 3, 2, -3, 4, -2, 3, -4, 5, 2, 2, 4, -5, 6, -2, -3, -2, 5, -6, 7, 2, 3, 3, 2, 6, -7, 8, -2, 2, -4, 2, -2, 7, -8, 9, 2, -3, 4, 4, -3, 2, 8, -9, 10, -2, 3, -2, -5, -2, 3, -2, 9, -10, 11, 2, 2, 3, 5, 5, 3, 2, 2, 10, -11, 12, -2, -3, -4, 2, -6, 2, -4, -3, -2, 11, -12, 13, 2, 3, 4, 2, 6, 6, 2

Offset

1,2

Comments

The function T(n, k) = T(k, n) is defined for k>n but only the values for 1 <= k <= n as a triangular array are listed here.

Links

G. C. Greubel, Rows n=1..100 of triangle, flattened

Formula

T(n, k) = - gcd(n, k) if gcd(n, k) > 1.

Example

{1}, {2, -2}, {3, 2, -3}, {4, -2, 3, -4}, {5, 2, 2, 4, -5}, {6, -2, -3, -2 ,5, -6}, ...

Mathematica

T[ n_, k_] := If[ n < 1 || k < 1, 0,  If[ k > n, T[ k, n], If[ k == 1, n, If[ n > k, T[ k, Mod[ n, k, 1]], -n]]]]

Prog

(PARI) {T(n, k) = if( n<1 || k<1, 0, if( k>n, T(k, n), if( k==1, n, if( n>k, T(k, (n-1)%k + 1), -n))))}

Crossrefs

Cf. A054521.

Sequence in context: A336346 A338283 A104324 * A131818 A222111 A222438

Adjacent sequences: A193209 A193210 A193211 * A193213 A193214 A193215

Keyword

sign,tabl

Author

Michael Somos, Jul 18 2011

Status

approved