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A351153
Triangle read by rows: T(n, k) = n*(k - 1) - k*(k - 3)/2 with 0 < k <= n.
14
1, 1, 3, 1, 4, 6, 1, 5, 8, 10, 1, 6, 10, 13, 15, 1, 7, 12, 16, 19, 21, 1, 8, 14, 19, 23, 26, 28, 1, 9, 16, 22, 27, 31, 34, 36, 1, 10, 18, 25, 31, 36, 40, 43, 45, 1, 11, 20, 28, 35, 41, 46, 50, 53, 55, 1, 12, 22, 31, 39, 46, 52, 57, 61, 64, 66, 1, 13, 24, 34, 43, 51, 58, 64, 69, 73, 76, 78
OFFSET
1,3
COMMENTS
Except for the number 2, it contains all the positive integers.
FORMULA
T(n, k) = 1 + Sum_{i=1..k-1} (n - i + 1).
From R. J. Mathar, Feb 07 2022: (Start)
G.f.: x*y*(1 - x + y*x^2 + y^2*x^3)/((1 - x)^2*(1 - y*x)^3).
T(n, k) = 1 + A141418(n+1, k-1) = 1 + A087401(n+1, k-1). (End)
EXAMPLE
Triangle begins:
1;
1, 3;
1, 4, 6;
1, 5, 8, 10;
1, 6, 10, 13, 15;
1, 7, 12, 16, 19, 21;
1, 8, 14, 19, 23, 26, 28;
...
MATHEMATICA
Flatten[Table[n(k-1)-k(k-3)/2, {n, 12}, {k, n}]]
CROSSREFS
Cf. A000012 (1st column), A000217 (leading diagonal), A005843 (3rd column), A006007 (sum of the first n rows), A006527 (row sums).
Sequence in context: A286159 A307394 A194540 * A193043 A086271 A345229
KEYWORD
nonn,easy,tabl
AUTHOR
Stefano Spezia, Feb 02 2022
STATUS
approved