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A084061 Square number array read by antidiagonals.

%I A084061 #15 Sep 08 2022 08:45:10
%S A084061 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 A084061 4400,46656,1,1,9,63,553,5725,66637,823543,1,1,10,72,656,7100,87704,
%U A084061 1188544,16777216,1,1,11,81,761,8525,109863,1577849,24405761,387420489,1,1,12,90,868,10000,133120,1991752,32618512,567108864,10000000000
%N A084061 Square number array read by antidiagonals.
%H A084061 G. C. Greubel, <a href="/A084061/b084061.txt">Antidiagonal rows n = 0..100, flattened</a>
%F A084061 T(n, k) = ( (n - sqrt(k))^n + (n + sqrt(k))^n )/2.
%e A084061 Rows begin:
%e A084061 1 1 4 27 256 ...
%e A084061 1 1 5 36 353 ...
%e A084061 1 1 6 45 452 ...
%e A084061 1 1 7 54 553 ...
%e A084061 1 1 8 63 656 ...
%p A084061 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 A084061 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 A084061 (PARI) T(n,k) = round( ((k+sqrt(n-k))^n + (k-sqrt(n-k))^k)/2 ); \\ _G. C. Greubel_, Jan 11 2020
%o A084061 (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 A084061 (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 A084061 (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 A084061 Rows include A000312, A062024, A084063, A084064, A084065.
%Y A084061 Diagonals include A084062, A084063, A084095.
%K A084061 nonn,tabl,easy
%O A084061 0,6
%A A084061 _Paul Barry_, May 11 2003