A084095 First superdiagonal of number array A084061.

1, 1, 5, 45, 553, 8525, 157481, 3383989, 82823777, 2272771305, 69070483549, 2301873355661, 83445967372681, 3268307044050997, 137510640882447041, 6184402325475261525, 296032663549928711041, 15025296455500536616337

Offset: 0

Author

Paul Barry, May 11 2003

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A084061, A084062, A084063, A084064, A084065, A084096.

Programs

GAP

List([0..20], n-> ((n-Sqrt(n-1))^n + (n+Sqrt(n-1))^n)/2); # G. C. Greubel, Jan 11 2020

Magma

[Round(((n-Sqrt(n-1))^n + (n+Sqrt(n-1))^n)/2): n in [0..20]]; // G. C. Greubel, Jan 11 2020

Maple

seq( round(((n-sqrt(n-1))^n + (n+sqrt(n-1))^n)/2), n=0..20); # G. C. Greubel, Jan 11 2020

Mathematica

Table[Round[((n+Sqrt[n-1])^n + (n-Sqrt[n-1])^n)/2], {n,0,20}] (* G. C. Greubel, Jan 11 2020 *)

PARI

vector(21, n, round(((n-1-sqrt(n-2))^(n-1) + (n-1+sqrt(n-2))^(n-1))/2) ) \\ G. C. Greubel, Jan 11 2020

Sage

[round(((n-sqrt(n-1))^n + (n+sqrt(n-1))^n)/2) for n in (0..20)] # G. C. Greubel, Jan 11 2020

Formula

a(n) = ((n - sqrt(n-1))^n + (n + sqrt(n-1))^n)/2.