OFFSET
1,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..11325 (first 150 antidiagonals, flattened).
FORMULA
T(n, k) = T(k, n), array is symmetric.
T(n, k) = 3*n*k - n*h(k) - k*h(n) where h(n) = ceiling(2*n / (sqrt(5) + 3)) = A189663(n + 1). - Peter Luschny, Mar 21 2024
EXAMPLE
Array begins:
1 3 4 6 8 ...
3 8 11 16 21 ...
4 11 15 22 29 ...
6 16 22 32 42 ...
8 21 29 42 55 ...
...
MAPLE
h := n -> ceil(2*n / (sqrt(5) + 3)):
T := (n, k) -> 3*n*k - n*h(k) - k*h(n):
seq(lprint(seq(T(n, k), k = 1..9)), n = 1..7); # Peter Luschny, Mar 21 2024
MATHEMATICA
A340429[n_, k_] := Floor[n * GoldenRatio] * k + Floor[k * GoldenRatio] * n - n * k;
Table[A340429[n - k + 1, k], {n, 15}, {k, n}] (* Paolo Xausa, Mar 21 2024 *)
PROG
(PARI) f(n) = 2*floor(n*(1+sqrt(5))/2) - 3*n; \\ A339765
T(n, k) = 2*n*k + f(n)*k/2 + f(k)*n/2;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Jan 07 2021
STATUS
approved