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A131225
Triangle read by rows: T(n,k) = 2*k - (1 + (-1)^(n-k))/2 (1 <= k <= n).
2
1, 2, 3, 1, 4, 5, 2, 3, 6, 7, 1, 4, 5, 8, 9, 2, 3, 6, 7, 10, 11, 1, 4, 5, 8, 9, 12, 13, 2, 3, 6, 7, 10, 11, 14, 15, 1, 4, 5, 8, 9, 12, 13, 16, 17, 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, 2, 3, 6, 7, 10, 11, 14, 15, 18, 19, 22, 23
OFFSET
1,2
COMMENTS
Row sums = A035608: (1, 5, 10, 18, 27, 39, ...).
FORMULA
2*A002260 - A128174, as infinite lower triangular matrices; where A002260 = (1; 1,2; 1,2,3; ...) and A128174 = (1; 0,1; 1,0,1; ...).
EXAMPLE
First few rows of the triangle:
1;
2, 3;
1, 4, 5;
2, 3, 6, 7;
1, 4, 5, 8, 9;
2, 3, 6, 7, 10, 11;
1, 4, 5, 8, 9, 12, 13;
...
MAPLE
T := proc (n, k) options operator, arrow; 2*k-1/2-(1/2)*(-1)^(n-k) end proc: for n to 10 do seq(T(n, k), k = 1 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jul 09 2007
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 20 2007
EXTENSIONS
a(47), a(49) corrected and more terms from Georg Fischer, Jun 07 2023
STATUS
approved