A084062 Main diagonal of number array A084061.

1, 1, 6, 54, 656, 10000, 182952, 3899224, 94769152, 2584929024, 78145100000, 2592261435104, 93586594074624, 3651967705305088, 153140949522798720, 6866498202750000000, 327772442129447518208, 16593897777705323921408

Offset: 0

Author

Paul Barry, May 11 2003

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..380

Crossrefs

Cf. A084063, A084095.

Programs

Magma

[1] cat [Round(( (n +Sqrt(n))^n + (n -Sqrt(n))^n )/2): n in [1..20]]; // G. C. Greubel, Jan 03 2020

Maple

seq( `if`(n=0, 1, round(( (n + sqrt(n))^n + (n - sqrt(n))^n )/2)), n=0..20); # G. C. Greubel, Jan 03 2020

Mathematica

Table[If[n==0, 1, Round[((n+Sqrt[n])^n + (n-Sqrt[n])^n)/2]], {n,0,20}] (* G. C. Greubel, Jan 03 2020 *)

PARI

vector(21, n, if(n==0, 1, round( ( (n-1 + sqrt(n-1))^(n-1) + (n-1 - sqrt(n-1))^(n-1) )/2 )) ) \\ G. C. Greubel, Jan 03 2020

Sage

[1]+[round(( (n +sqrt(n))^n + (n -sqrt(n))^n )/2) for n in (1..30)] # G. C. Greubel, Jan 03 2020

Formula

a(n) = ( (n + sqrt(n))^n + (n - sqrt(n))^n )/2.