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

0,3

Links

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

Formula

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

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 *)

Prog

(PARI) vector(21, n, round(((n-1-sqrt(2))^(n-1) + (n-1+sqrt(2))^(n-1))/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
(Sage) [round(((n-sqrt(2))^n + (n+sqrt(2))^n)/2) for n in (0..20)] # G. C. Greubel, Jan 11 2020
(GAP) List([0..20], n-> ((n-Sqrt(2))^n + (n+Sqrt(2))^n)/2); # G. C. Greubel, Jan 11 2020

Crossrefs

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

Sequence in context: A239910 A228194 A331726 * A186925 A368793 A294642

Adjacent sequences: A084061 A084062 A084063 * A084065 A084066 A084067

Keyword

nonn,easy

Author

Paul Barry, May 11 2003

Status

approved