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%I #9 Sep 08 2022 08:45:10
%S 1,1,6,54,656,10000,182952,3899224,94769152,2584929024,78145100000,
%T 2592261435104,93586594074624,3651967705305088,153140949522798720,
%U 6866498202750000000,327772442129447518208,16593897777705323921408
%N Main diagonal of number array A084061.
%H G. C. Greubel, <a href="/A084062/b084062.txt">Table of n, a(n) for n = 0..380</a>
%F a(n) = ( (n + sqrt(n))^n + (n - sqrt(n))^n )/2.
%p seq( `if`(n=0, 1, round(( (n + sqrt(n))^n + (n - sqrt(n))^n )/2)), n=0..20); # _G. C. Greubel_, Jan 03 2020
%t Table[If[n==0, 1, Round[((n+Sqrt[n])^n + (n-Sqrt[n])^n)/2]], {n,0,20}] (* _G. C. Greubel_, Jan 03 2020 *)
%o (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
%o (Magma) [1] cat [Round(( (n +Sqrt(n))^n + (n -Sqrt(n))^n )/2): n in [1..20]]; // _G. C. Greubel_, Jan 03 2020
%o (Sage) [1]+[round(( (n +sqrt(n))^n + (n -sqrt(n))^n )/2) for n in (1..30)] # _G. C. Greubel_, Jan 03 2020
%Y Cf. A084063, A084095.
%K easy,nonn
%O 0,3
%A _Paul Barry_, May 11 2003
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