A084064 Third row of number array A084061.

1, 1, 6, 45, 452, 5725, 87704, 1577849, 32618512, 762046137, 19856872032, 571007744549, 17962793210944, 613650073693397, 22624291883495808, 895379458590349425, 37861032312753094912, 1703550488551604490353

Offset: 0

Author

Paul Barry, May 11 2003

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000312, A062024, A084061, A084062, A084063, A084065, A084095, A084096.

Programs

GAP

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

Magma

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

Maple

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

Mathematica

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

PARI

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

Sage

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

Formula

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