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A293375 Triangle read by rows: T(n, k), for 1 <= k <= n, where T(n, k) is defined in A192763. 0
1, 2, -2, 1, 2, -3, 1, -2, 1, 0, 0, 2, 2, 1, -5, 1, -2, -3, -2, 0, 6, 0, 2, 1, 1, 2, 1, -7, 0, -2, 2, 0, 2, -2, 0, 0, 0, 2, -3, 1, 1, -3, 2, 0, 0, 1, -2, 1, -2, -5, -2, 1, -2, 0, 10, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, -11, 0, -2, -3, 0, 2, 6, 2, 0, -3, -2, 0, 0, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..79.

M. Granvik, Is this a recurrence for the Mertens function plus 2?, Math StackExchange question 50719.

EXAMPLE

Triangle begins:

1;

2, -2;

1,  2, -3;

1, -2,  1,  0;

0,  2,  2,  1, -5;

1, -2, -3, -2,  0, 6;

...

MATHEMATICA

T[ n_, k_] := Which[ n < 1 || k < 1, 0, k > n, T[ k, n], k == 1, If[ n < 3, n, (n T[ n - 1, 1] - Sum[ T[ n, i], {i, 2, n - 1}]) / (n + 1)], n > k , T[ k, Mod[ n, k, 1]], True, - Sum[ T[ n, i], {i, n - 1}]];

PROG

(PARI) {T(n, k) = if( n<1 || k<1, 0, k>n, T(k, n), k==1, if( n<3, n, (n * T(n-1, 1) - sum( i=2, n-1, T(n, i))) / (n+1)), n>k, T(k, (n-1)%k+1), -sum( i=1, n-1, T(n, i)))};

CROSSREFS

Cf. A192763.

Sequence in context: A345764 A236573 A333252 * A232174 A077766 A273110

Adjacent sequences:  A293372 A293373 A293374 * A293376 A293377 A293378

KEYWORD

sign,tabl

AUTHOR

Michael Somos, Oct 07 2017

STATUS

approved

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Last modified January 23 07:56 EST 2022. Contains 350510 sequences. (Running on oeis4.)