A084065 Fourth row of number array A084061.

1, 1, 7, 54, 553, 7100, 109863, 1991752, 41426257, 972602640, 25447064743, 734276705888, 23166635069241, 793426715543488, 29316839407495111, 1162492244159875200, 49240280161094287777, 2218952409252783579392

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, A084095, A084096.

Programs

GAP

List([0..20], n-> ((n-Sqrt(3))^n + (n+Sqrt(3))^n)/2); # G. C. Greubel, Jan 11 2020

Magma

[Round(((n-Sqrt(3))^n + (n+Sqrt(3))^n)/2): n in [0..20]]; // G. C. Greubel, Jan 11 2020

Maple

seq( round(((n-sqrt(3))^n + (n+sqrt(3))^n)/2), n=0..20); # G. C. Greubel, Jan 11 2020

Mathematica

Table[Round[((n+Sqrt[3])^n + (n-Sqrt[3])^n)/2], {n,0,20}] (* G. C. Greubel, Jan 11 2020 *)

PARI

vector(21, n, round(((n-1-sqrt(3))^(n-1) + (n-1+sqrt(3))^(n-1))/2) ) \\ G. C. Greubel, Jan 11 2020

Sage

[round(((n-sqrt(3))^n + (n+sqrt(3))^n)/2) for n in (0..20)] # G. C. Greubel, Jan 11 2020

Formula

a(n) = ( (n - sqrt(3))^n + (n + sqrt(3))^n )/2.