A322744 Array T(n,k) = (3*n*k - A319929(n,k))/2, n >= 1, k >= 1, read by antidiagonals.
1, 2, 2, 3, 6, 3, 4, 8, 8, 4, 5, 12, 11, 12, 5, 6, 14, 16, 16, 14, 6, 7, 18, 19, 24, 19, 18, 7, 8, 20, 24, 28, 28, 24, 20, 8, 9, 24, 27, 36, 33, 36, 27, 24, 9, 10, 26, 32, 40, 42, 42, 40, 32, 26, 10, 11, 30, 35, 48, 47, 54, 47, 48, 35, 30, 11, 12, 32, 40, 52, 56, 60, 60, 56, 52, 40, 32, 12
Offset: 1
Examples
Array T(n,k) begins: 1 2 3 4 5 6 7 8 9 10 2 6 8 12 14 18 20 24 26 30 3 8 11 16 19 24 27 32 35 40 4 12 16 24 28 36 40 48 52 60 5 14 19 28 33 42 47 56 61 70 6 18 24 36 42 54 60 72 78 90 7 20 27 40 47 60 67 80 87 100 8 24 32 48 56 72 80 96 104 120 9 26 35 52 61 78 87 104 113 130 10 30 40 60 70 90 100 120 130 150
Links
- David Lovler, Table of n, a(n) for n = 1..861 (Antidiagonals n = 1..41, flattened)
Crossrefs
Programs
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Mathematica
Table[Function[n, (3 n k - If[OddQ@ n, If[OddQ@ k, n + k - 1, k], If[OddQ@ k, n, 0]])/2][m - k + 1], {m, 12}, {k, m}] // Flatten (* Michael De Vlieger, Apr 21 2019 *) -
PARI
T319929(n, k) = if (n%2, if (k%2, n+k-1, k), if (k%2, n, 0)); T(n,k) = (3*n*k - T319929(n,k))/2; matrix(6, 6, n, k, T(n, k)) \\ Michel Marcus, Dec 27 2018
Formula
T(n,k) = (3*n*k - (n + k - 1))/2 if n is odd and k is odd;
T(n,k) = (3*n*k - n)/2 if n is even and k is odd;
T(n,k) = (3*n*k - k)/2 if n is odd and k is even;
T(n,k) = 3*n*k/2 if n is even and k is even.
T(n,k) = 6*floor(n/2)*floor(k/2) + A319929(n,k).
T(n,n) = A354594(n). - David Lovler, Jul 09 2022
Comments