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A275015 Number of neighbors of each new term in an isosceles triangle read by rows. 4
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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

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

If every "3" is replaced with a "4", we have the sequence A278290.

a(n) is also the number of new penny-penny contacts when putting pennies in a triangular arrangement.

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.

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

The sequence written as an isosceles triangle begins:

.

.                     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,  3,  2;

.     1,  3,  3,  3,  3,  3,  3,  3,  2;

.   1,  3,  3,  3,  3,  3,  3,  3,  3,  2;

...

MATHEMATICA

Table[Boole[n > 1] (Prepend[Reverse@ Rest@ #, First@ #] &@ Range@ n /. k_ /; k > 3 -> 3), {n, 13}] // Flatten (* or *)

Table[Boole[n > 1] (Map[Mod[#, n] &, Range@ n] /. {k_ /; k > 1 -> 3, 0 -> 2}), {n, 13}] // Flatten (* Michael De Vlieger, Nov 23 2016 *)

CROSSREFS

Row sums give A008585.

Left border gives A057427.

Every diagonal that is parallel to the left border gives the elements greater than 1 of A158799.

Right border gives 0 together with A007395, also twice A057427.

Every diagonal that is parallel to the right border gives A122553.

Cf. A047931, A278290, A278317, A278354.

Sequence in context: A113787 A115624 A076291 * A211189 A194968 A194980

Adjacent sequences:  A275012 A275013 A275014 * A275016 A275017 A275018

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Nov 20 2016

STATUS

approved

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)