OFFSET
0,6
LINKS
G. C. Greubel, Antidiagonal rows n = 0..100, flattened
FORMULA
T(n, k) = ( (n - sqrt(k))^n + (n + sqrt(k))^n )/2.
EXAMPLE
Rows begin:
1 1 4 27 256 ...
1 1 5 36 353 ...
1 1 6 45 452 ...
1 1 7 54 553 ...
1 1 8 63 656 ...
MAPLE
seq(seq( round(((k+sqrt(n-k))^k + (k-sqrt(n-k))^k)/2), k=0..n), n=0..10); # G. C. Greubel, Jan 11 2020
MATHEMATICA
Table[If[n==0 && k==0, 1, Round[((k-Sqrt[n-k])^k + (k+Sqrt[n-k])^k)/2]], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Jan 11 2020 *)
PROG
(PARI) T(n, k) = round( ((k+sqrt(n-k))^n + (k-sqrt(n-k))^k)/2 ); \\ G. C. Greubel, Jan 11 2020
(Magma) [Round(((k+Sqrt(n-k))^k + (k-Sqrt(n-k))^k)/2): k in [0..n], n in [0..10]]; // G. C. Greubel, Jan 11 2020
(Sage) [[round(((k+sqrt(n-k))^k + (k-sqrt(n-k))^k)/2) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Jan 11 2020
(GAP) Flat(List([0..10], n-> List([0..n], k-> ((k+Sqrt(n-k))^k + (k-Sqrt(n-k))^k)/2 ))); # G. C. Greubel, Jan 11 2020
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, May 11 2003
STATUS
approved