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A084061 Square number array read by antidiagonals. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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

Diagonals include A084062, A084063, A084095.

Sequence in context: A114033 A209417 A267990 * A140262 A049702 A159040

Adjacent sequences:  A084058 A084059 A084060 * A084062 A084063 A084064

KEYWORD

nonn,tabl,easy

AUTHOR

Paul Barry, May 11 2003

STATUS

approved

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Last modified January 29 10:34 EST 2020. Contains 331337 sequences. (Running on oeis4.)