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A278545 Number of neighbors of the n-th term in a full square array read by antidiagonals. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

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

FORMULA

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

EXAMPLE

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,...

...

MAPLE

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

CROSSREFS

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

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

Sequence in context: A141791 A196158 A290561 * A023828 A120133 A088961

Adjacent sequences:  A278542 A278543 A278544 * A278546 A278547 A278548

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Nov 23 2016

STATUS

approved

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Last modified September 23 14:40 EDT 2021. Contains 347618 sequences. (Running on oeis4.)