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A279416 Triangle read by rows: T(n,k), n>=k>=1, is the number of grid points below the diagonal of a (n X k)-grid. 2
0, 0, 1, 0, 2, 3, 0, 3, 5, 6, 0, 4, 6, 9, 10, 0, 5, 8, 11, 14, 15, 0, 6, 9, 12, 16, 20, 21, 0, 7, 11, 15, 19, 23, 27, 28, 0, 8, 12, 17, 20, 26, 30, 35, 36, 0, 9, 14, 18, 24, 29, 33, 39, 44, 45, 0, 10, 15, 21, 26, 30, 37, 43, 48, 54, 55, 0, 11, 17, 23, 29, 35 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

T(n,1) = 0, T(n,n) = A000217(n-1) = n*(n-1)/2.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..9870 (the first 140 rows)

FORMULA

T(n,k) = (k * n - (gcd(n - 1, k - 1) + 1)) / 2.

EXAMPLE

Triangle begins:

0

0,1

0,2,3

0,3,5,6

0,4,6,9,10

0,5,8,11,14,15

0,6,9,12,16,20,21

0,7,11,15,19,23,27,28

0,8,12,17,20,26,30,35,36

0,9,14,18,24,29,33,39,44,45

0,10,15,21,26,30,37,43,48,54,55

0,11,17,23,29,35,41,47,53,59,65,66

0,12,18,24,30,38,42,51,56,63,70,77,78

0,13,20,27,34,41,48,55,62,69,76,83,90,91

0,14,21,29,36,44,51,56,66,74,81,89,96,104,105

0,15,23,30,39,45,54,63,71,78,85,95,102,111,119,120

0,16,24,33,40,50,58,67,72,84,92,101,108,118,126,135,136

0,17,26,35,44,53,62,71,80,89,98,107,116,125,134,143,152,153

0,18,27,36,46,56,63,75,84,90,103,113,120,132,141,150,160,170,171

0,19,29,39,49,59,69,79,89,99,109,119,129,139,149,159,169,179,189,190

MATHEMATICA

Table[(k n - (GCD[n - 1, k - 1] + 1))/2, {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Feb 22 2017 *)

CROSSREFS

Cf A279417.

Sequence in context: A224909 A227536 A047773 * A187988 A035549 A329970

Adjacent sequences:  A279413 A279414 A279415 * A279417 A279418 A279419

KEYWORD

nonn,tabl,easy

AUTHOR

Lars Blomberg, Feb 22 2017

STATUS

approved

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Last modified January 21 05:23 EST 2020. Contains 331104 sequences. (Running on oeis4.)