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A234248 Number of distinct lines passing through at least three points in a triangular grid of side n. 3
3, 6, 12, 21, 36, 57, 90, 129, 186, 261, 354, 465, 612, 783, 990, 1233, 1524, 1863, 2262, 2703, 3216, 3801, 4458, 5187, 6024, 6951, 7986, 9129, 10392, 11775, 13302, 14943, 16746, 18711, 20844, 23145, 25668, 28377, 31296, 34425, 37782, 41367, 45210, 49287 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Jon E. Schoenfield, Table of n, a(n) for n = 3..10000

FORMULA

a(n) = 3*Sum_{j=1..floor((n-1)/(k-1))} EulerPhi(j) * (g(n-(k-1)*j) - g(n-k*j)) where k = 3 (the minimum required number of points) and g(i) = A000217(i) (i.e., the i-th triangular number) if i > 0, otherwise 0. - Jon E. Schoenfield, Aug 17 2014

EXAMPLE

     a

    b c

   d e f

  g h i j

In this triangle grid of side 4, there are a(4) = 6 distinct lines passing through at least 3 points: ag, gj, ja, ch, df, ib.

PROG

(PARI) g(n) = if (n>0, n*(n+1)/2, 0);

a(n) = my(k=3); 3*sum(j=1, (n-1)\(k-1), eulerphi(j) * (g(n-(k-1)*j) - g(n-k*j))); \\ Michel Marcus, Aug 19 2014

CROSSREFS

Cf. A225606 (analogous problem for square grids).

Sequence in context: A203292 A054578 A115855 * A294387 A128128 A162920

Adjacent sequences:  A234245 A234246 A234247 * A234249 A234250 A234251

KEYWORD

nonn,nice

AUTHOR

Heinrich Ludwig, Jan 18 2014

EXTENSIONS

More terms from Jon E. Schoenfield, Aug 17 2014

STATUS

approved

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Last modified November 14 12:14 EST 2019. Contains 329113 sequences. (Running on oeis4.)