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A113125
A simple tridiagonal matrix.
1
1, 1, 2, 1, 2, 3, 0, 2, 3, 4, 0, 0, 3, 4, 5, 0, 0, 0, 4, 5, 6, 0, 0, 0, 0, 5, 6, 7, 0, 0, 0, 0, 0, 6, 7, 8, 0, 0, 0, 0, 0, 0, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 8, 9, 10, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
OFFSET
0,3
COMMENTS
Row sums are A008486 (coordination sequence for graphite net). Diagonal sums are A026741(n+1). Diagonals are A000027.
FORMULA
Number triangle where column k has g.f. (1+x+x^2)(k+1)x^k.
EXAMPLE
Triangle begins
1;
1, 2;
1, 2, 3;
0, 2, 3, 4;
0, 0, 3, 4, 5;
0, 0, 0, 4, 5, 6;
0, 0, 0, 0, 5, 6, 7;
0, 0, 0, 0, 0, 6, 7, 8;
MATHEMATICA
Table[If[#<(n-2), 0, #]&/@Range[n], {n, 15}]//Flatten (* Harvey P. Dale, Oct 14 2022 *)
CROSSREFS
Cf. A113126.
Sequence in context: A364880 A141455 A292627 * A088239 A130070 A273516
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Oct 14 2005
STATUS
approved