A278481 -id:A278481 - cp's OEIS frontend

A278597 One half of A278481.

1, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2

Offset: 1

Omar E. Pol, Nov 23 2016

Apart from the left border and the right border, the rest of the elements are 3's.

			The sequence written as a triangle begins:
                      1;
                    2,  2;
                  2,  3,  2;
                2,  3,  3,  2;
              2,  3,  3,  3,  2;
            2,  3,  3,  3,  3,  2;
          2,  3,  3,  3,  3,  3,  2;
        2,  3,  3,  3,  3,  3,  3,  2;
      2,  3,  3,  3,  3,  3,  3,  3,  2;
    2,  3,  3,  3,  3,  3,  3,  3,  3,  2;
  ...

Row sums give A016777.
Left border gives A040000, the same as the right border.
Middle column gives A122553.
Every diagonal that is parallel to any of the borders gives the elements greater than 1 of A158799.
Cf. A278481.

a(n) = A278481(n)/2.

A278480 Number of neighbors of the n-th term in a full right triangle read by rows.

Original entry on oeis.org

2, 4, 5, 5, 7, 5, 5, 8, 7, 5, 5, 8, 8, 7, 5, 5, 8, 8, 8, 7, 5, 5, 8, 8, 8, 8, 7, 5, 5, 8, 8, 8, 8, 8, 7, 5, 5, 8, 8, 8, 8, 8, 8, 7, 5, 5, 8, 8, 8, 8, 8, 8, 8, 7, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 7, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 5

Offset: 1

Omar E. Pol, Nov 23 2016

Apart from the first column and the first two diagonals, the rest of the elements are 8's.

For the same idea but for an isosceles triangle see A278481; for a square array see A278545, for a square spiral see A010731; and for a hexagonal spiral see A010722.

			The sequence written as a right triangle begins:
2;
4, 5;
5, 7, 5;
5, 8, 7, 5;
5, 8, 8, 7, 5;
5, 8, 8, 8, 7, 5;
5, 8, 8, 8, 8, 7, 5;
5, 8, 8, 8, 8, 8, 7, 5;
5, 8, 8, 8, 8, 8, 8, 7, 5;
5, 8, 8, 8, 8, 8, 8, 8, 7, 5;
...

Row sums give 2 together with the elements > 1 of A017077.
Also, row sums give 2 together with A004768.
Cf. A010722, A010731, A278317, A278481, A278545.

A278545 Number of neighbors of the n-th term in a full square array read by antidiagonals.

Original entry on oeis.org

3, 5, 5, 5, 8, 5, 5, 8, 8, 5, 5, 8, 8, 8, 5, 5, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5

Offset: 1

Omar E. Pol, Nov 23 2016

Apart from the first row and the first column, the rest of the elements are 8's.

For the same idea but for a right triangle see A278480; for an isosceles triangle see A278481; for a square spiral see A010731; and for a hexagonal spiral see A010722.

			The corner of the square array begins:
3,5,5,5,5,5,5,5,5,5,...
5,8,8,8,8,8,8,8,8,...
5,8,8,8,8,8,8,8,...
5,8,8,8,8,8,8,...
5,8,8,8,8,8,...
5,8,8,8,8,...
5,8,8,8,...
5,8,8,...
5,8,...
5,...
...

Robert Israel, Table of n, a(n) for n = 1..10000

Antidiagonal sums give 3 together with the elements > 2 of A017089.

Cf. A010722, A010731, A274912, A274913, A278317, A278290, A278480, A278481.

3, seq(op([5,8$i,5]),i=0..20); # Robert Israel, Dec 04 2016

G.f. 3+x+8*x/(1-x)-3*(1+x)*Theta_2(0,sqrt(x))/(2*x^(1/8)) where Theta_2 is a Jacobi Theta function. - Robert Israel, Dec 04 2016

cp's OEIS Frontend

A278597 One half of A278481.

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A278480 Number of neighbors of the n-th term in a full right triangle read by rows.

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A278545 Number of neighbors of the n-th term in a full square array read by antidiagonals.

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