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

0,3

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A189122 A062023 A169714 * A174495 A121414 A243678

Adjacent sequences: A084092 A084093 A084094 * A084096 A084097 A084098

Keyword

easy,nonn

Author

Paul Barry, May 11 2003

Status

approved