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 A351153 Triangle read by rows: T(n, k) = n*(k - 1) - k*(k - 3)/2 with 0 < k <= n. 13
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Except for the number 2, it contains all the positive integers. LINKS 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). Cf. A087401, A141418, A351154. Sequence in context: A286159 A307394 A194540 * A193043 A086271 A345229 Adjacent sequences: A351150 A351151 A351152 * A351154 A351155 A351156 KEYWORD nonn,easy,tabl AUTHOR Stefano Spezia, Feb 02 2022 STATUS approved

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Last modified March 28 23:19 EDT 2023. Contains 361596 sequences. (Running on oeis4.)