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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 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.)