A084061 - OEIS

%I #15 Sep 08 2022 08:45:10

%S 1,1,1,1,1,4,1,1,5,27,1,1,6,36,256,1,1,7,45,353,3125,1,1,8,54,452,

%T 4400,46656,1,1,9,63,553,5725,66637,823543,1,1,10,72,656,7100,87704,

%U 1188544,16777216,1,1,11,81,761,8525,109863,1577849,24405761,387420489,1,1,12,90,868,10000,133120,1991752,32618512,567108864,10000000000

%N Square number array read by antidiagonals.

%H G. C. Greubel, <a href="/A084061/b084061.txt">Antidiagonal rows n = 0..100, flattened</a>

%F T(n, k) = ( (n - sqrt(k))^n + (n + sqrt(k))^n )/2.

%e Rows begin:

%e 1 1 4 27 256 ...

%e 1 1 5 36 353 ...

%e 1 1 6 45 452 ...

%e 1 1 7 54 553 ...

%e 1 1 8 63 656 ...

%p 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

%t 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 *)

%o (PARI) T(n,k) = round( ((k+sqrt(n-k))^n + (k-sqrt(n-k))^k)/2 ); \\ _G. C. Greubel_, Jan 11 2020

%o (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

%o (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

%o (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

%Y Rows include A000312, A062024, A084063, A084064, A084065.

%Y Diagonals include A084062, A084063, A084095.

%K nonn,tabl,easy

%O 0,6

%A _Paul Barry_, May 11 2003