OFFSET

1,7

COMMENTS

LINKS

David Applegate, Table of n, a(n) for n = 1..800

David Applegate, Triangular table T(n,k) for n = 1..100

N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)

N. J. A. Sloane (in collaboration with Scott R. Shannon), Art and Sequences, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.

FORMULA

Sum_{k} T(n,k) * binomial(k,2) = binomial(n,4), because there are binomial(n,4) total pairs of semicircles, and an intersection of k consists of binomial(k,2) of those pairs.

A290865(n) = binomial(n,2) + Sum_{k} T(n,k) * (k-1).

EXAMPLE

Triangle begins:

0;

0;

0;

0, 1;

0, 5;

0, 15;

0, 35;

0, 70;

0, 123, 1;

0, 195, 5;

0, 285, 15;

0, 420, 25;

0, 586, 39, 2;

CROSSREFS

KEYWORD

nonn,tabf

AUTHOR

David Applegate, Aug 12 2017

STATUS

approved