cp's OEIS Frontend

A275015 Number of neighbors of each new term in an isosceles triangle read by rows.

%I A275015 #49 Apr 24 2018 05:52:24
%S A275015 0,1,2,1,3,2,1,3,3,2,1,3,3,3,2,1,3,3,3,3,2,1,3,3,3,3,3,2,1,3,3,3,3,3,
%T A275015 3,2,1,3,3,3,3,3,3,3,2,1,3,3,3,3,3,3,3,3,2,1,3,3,3,3,3,3,3,3,3,2,1,3,
%U A275015 3,3,3,3,3,3,3,3,3,2,1,3,3,3,3,3,3,3,3,3,3,3,2,1,3,3,3,3,3,3,3,3,3,3,3,3,2
%N A275015 Number of neighbors of each new term in an isosceles triangle read by rows.
%C A275015 To evaluate a(n) consider only the neighbors of a(n) that are present in the isosceles triangle when a(n) should be a new term in the triangle.
%C A275015 Apart from the left border and the right border, the rest of the elements are 3's.
%C A275015 If every "3" is replaced with a "4", we have the sequence A278290.
%C A275015 a(n) is also the number of new penny-penny contacts when putting pennies in a triangular arrangement.
%C A275015 For the same idea but for a right triangle see A278317; for a square array see A278290, for a square spiral see A278354; and for a hexagonal spiral see A047931.
%e A275015 The sequence written as an isosceles triangle begins:
%e A275015 .
%e A275015 .                     0;
%e A275015 .                   1,  2;
%e A275015 .                 1,  3,  2;
%e A275015 .               1,  3,  3,  2;
%e A275015 .             1,  3,  3,  3,  2;
%e A275015 .           1,  3,  3,  3,  3,  2;
%e A275015 .         1,  3,  3,  3,  3,  3,  2;
%e A275015 .       1,  3,  3,  3,  3,  3,  3,  2;
%e A275015 .     1,  3,  3,  3,  3,  3,  3,  3,  2;
%e A275015 .   1,  3,  3,  3,  3,  3,  3,  3,  3,  2;
%e A275015 ...
%t A275015 Table[Boole[n > 1] (Prepend[Reverse@ Rest@ #, First@ #] &@ Range@ n /. k_ /; k > 3 -> 3), {n, 13}] // Flatten (* or *)
%t A275015 Table[Boole[n > 1] (Map[Mod[#, n] &, Range@ n] /. {k_ /; k > 1 -> 3, 0 -> 2}), {n, 13}] // Flatten (* _Michael De Vlieger_, Nov 23 2016 *)
%Y A275015 Row sums give A008585.
%Y A275015 Left border gives A057427.
%Y A275015 Every diagonal that is parallel to the left border gives the elements greater than 1 of A158799.
%Y A275015 Right border gives 0 together with A007395, also twice A057427.
%Y A275015 Every diagonal that is parallel to the right border gives A122553.
%Y A275015 Cf. A047931, A278290, A278317, A278354.
%K A275015 nonn,tabl
%O A275015 1,3
%A A275015 _Omar E. Pol_, Nov 20 2016