A245251 - OEIS

A245251

Triangle T(a,b) read by rows: sum_{k=1..a-1} floor(k*b/a).

0, 0, 1, 0, 1, 3, 0, 2, 3, 6, 0, 2, 4, 6, 10, 0, 3, 6, 8, 10, 15, 0, 3, 6, 9, 12, 15, 21, 0, 4, 7, 12, 14, 18, 21, 28, 0, 4, 9, 12, 16, 21, 24, 28, 36, 0, 5, 9, 14, 20, 23, 27, 32, 36, 45, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 55, 0, 6, 12, 18, 22, 30, 33, 40, 45, 50, 55, 66, 0, 6, 12, 18, 24, 30, 36, 45

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..86.

FORMULA

T(a, b) = (a*b-a-b+gcd(a,b))/2.

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

EXAMPLE

0 1;

0 1 3;

0 2 3 6;

0 2 4 6 10;

0 3 6 8 10 15;

0 3 6 9 12 15 21;

0 4 7 12 14 18 21 28;

0 4 9 12 16 21 24 28 36;

0 5 9 14 20 23 27 32 36 45;

MATHEMATICA

Table[Sum[Floor[(k b)/a], {k, a-1}], {a, 20}, {b, a}] // Flatten

CROSSREFS

Cf. A000217 (right diagonal).

Sequence in context: A112455 A001608 A159977 * A177461 A201924 A112974

Adjacent sequences: A245248 A245249 A245250 * A245252 A245253 A245254

KEYWORD

nonn,tabl,easy

AUTHOR

Jaimal Ichharam, Jul 15 2014

STATUS

approved