A327259 Array T(n,k) = 2*n*k - A319929(n,k), n >= 1, k >= 1, read by antidiagonals.
1, 2, 2, 3, 8, 3, 4, 10, 10, 4, 5, 16, 13, 16, 5, 6, 18, 20, 20, 18, 6, 7, 24, 23, 32, 23, 24, 7, 8, 26, 30, 36, 36, 30, 26, 8, 9, 32, 33, 48, 41, 48, 33, 32, 9, 10, 34, 40, 52, 54, 54, 52, 40, 34, 10, 11, 40, 43, 64, 59, 72, 59, 64, 43, 40, 11, 12, 42, 50, 68, 72, 78, 78, 72, 68, 50, 42, 12
Offset: 1
Examples
Array T(n,k) begins: 1 2 3 4 5 6 7 8 9 10 2 8 10 16 18 24 26 32 34 40 3 10 13 20 23 30 33 40 43 50 4 16 20 32 36 48 52 64 68 80 5 18 23 36 41 54 59 72 77 90 6 24 30 48 54 72 78 96 102 120 7 26 33 52 59 78 85 104 111 130 8 32 40 64 72 96 104 128 136 160 9 34 43 68 77 102 111 136 145 170 10 40 50 80 90 120 130 160 170 200
Links
- David Lovler, Table of n, a(n) for n = 1..465 [restored by _Georg Fischer_, Oct 14 2019]
Crossrefs
Programs
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Mathematica
T[n_,k_]:=2n*k-If[Mod[n,2]==1,If[Mod[k,2]==1,n+k-1,k],If[Mod[k,2]==1,n,0]]; MatrixForm[Table[T[n,k],{n,1,10},{k,1,10}]] (* Stefano Spezia, Sep 05 2019 *) -
PARI
T(n,k) = 2*n*k - if (n%2, if (k%2, n+k-1, k), if (k%2, n, 0)); matrix(8, 8, n, k, T(n,k)) \\ Michel Marcus, Sep 04 2019
Formula
T(n,k) = 2*n*k - n - k + 1 if n is odd and k is odd;
T(n,k) = 2*n*k - n if n is even and k is odd;
T(n,k) = 2*n*k - k if n is odd and k is even;
T(n,k) = 2*n*k if n is even and k is even.
T(n,k) = 8*floor(n/2)*floor(k/2) + A319929(n,k).
T(n,n) = A354595(n). - David Lovler, Jul 09 2022
Writing T(n,k) as (4*n*k - 2*A319929(n,k))/2 shows that the array is U(4;n,k) of A327263. - David Lovler, Jan 15 2022
Comments