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, 887974405536011279095296, 50075543848237101201106432

Offset

0,3

Links

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

Formula

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

a(n) ~ exp(n^(1/2) - 1/2 + 1/(3*n^(1/2)) - 1/(4*n) + 1/(5*n^(3/2))) * n^n / 2. - Amiram Eldar, Feb 09 2026

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 *)

Prog

(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
(Magma) [1] cat [Round(( (n +Sqrt(n))^n + (n -Sqrt(n))^n )/2): n in [1..20]]; // G. C. Greubel, Jan 03 2020
(SageMath) [1]+[round(( (n +sqrt(n))^n + (n -sqrt(n))^n )/2) for n in (1..30)] # G. C. Greubel, Jan 03 2020

Crossrefs

Cf. A084061, A084063, A084095.

Sequence in context: A081132 A158831 A034001 * A292633 A357309 A137591

Adjacent sequences: A084059 A084060 A084061 * A084063 A084064 A084065

Keyword

easy,nonn

Author

Paul Barry, May 11 2003

Status

approved