A084061 Square number array read by antidiagonals.
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, 4400, 46656, 1, 1, 9, 63, 553, 5725, 66637, 823543, 1, 1, 10, 72, 656, 7100, 87704, 1188544, 16777216, 1, 1, 11, 81, 761, 8525, 109863, 1577849, 24405761, 387420489, 1, 1, 12, 90, 868, 10000, 133120, 1991752, 32618512, 567108864, 10000000000
Offset: 0
Examples
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 ...
Links
- G. C. Greubel, Antidiagonal rows n = 0..100, flattened
Crossrefs
Programs
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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
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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
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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
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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 *) -
PARI
T(n,k) = round( ((k+sqrt(n-k))^n + (k-sqrt(n-k))^k)/2 ); \\ G. C. Greubel, Jan 11 2020
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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
Formula
T(n, k) = ( (n - sqrt(k))^n + (n + sqrt(k))^n )/2.