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A132918
Identity matrix with interpolated zeros.
1
1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1,1
COMMENTS
Identity matrix with interpolated zeros, such that the diagonal of an infinite lower triangular matrix = (1, 0, 1, 0, 1, ...) with the rest zeros.
Given A132918 = matrix M, then M * any sequence as a vector replaces alternate terms with zeros; e.g., M * [1,2,3,...] = [1,0,3,0,5,...]. M * (any infinite lower triangular matrix) replaces alternate rows with zeros; e.g., M * A007318 = (1; 0,0; 1,2,1; 0,0,0,0; ...).
a(n) = 1 if n is a positive hexagonal number, A000384: (1, 6, 15, 28, 45, 66, ...); zero otherwise.
EXAMPLE
First few rows of the triangle:
1;
0, 0;
0, 0, 1;
0, 0, 0, 0;
0, 0, 0, 0, 1;
...
PROG
(PARI) a(n) = ispolygonal(n, 6); \\ Michel Marcus, Aug 04 2023
CROSSREFS
Sequence in context: A015959 A014834 A015659 * A358750 A205809 A353370
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Sep 05 2007
EXTENSIONS
More terms from Michel Marcus, Mar 06 2022
STATUS
approved