A278545 - OEIS

%I #23 Dec 05 2016 05:00:30

%S 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,

%T 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,

%U 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

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

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

%C 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.

%H Robert Israel, <a href="/A278545/b278545.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%e The corner of the square array begins:

%e 3,5,5,5,5,5,5,5,5,5,...

%e 5,8,8,8,8,8,8,8,8,...

%e 5,8,8,8,8,8,8,8,...

%e 5,8,8,8,8,8,8,...

%e 5,8,8,8,8,8,...

%e 5,8,8,8,8,...

%e 5,8,8,8,...

%e 5,8,8,...

%e 5,8,...

%e 5,...

%e ...

%p 3, seq(op([5,8$i,5]),i=0..20); # _Robert Israel_, Dec 04 2016

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

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

%K nonn,tabl

%O 1,1

%A _Omar E. Pol_, Nov 23 2016