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%I #11 Sep 08 2022 08:45:10
%S 1,1,6,45,452,5725,87704,1577849,32618512,762046137,19856872032,
%T 571007744549,17962793210944,613650073693397,22624291883495808,
%U 895379458590349425,37861032312753094912,1703550488551604490353
%N Third row of number array A084061.
%H G. C. Greubel, <a href="/A084064/b084064.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = ( (n - sqrt(2))^n + (n + sqrt(2))^n )/2.
%p seq( round(((n-sqrt(2))^n + (n+sqrt(2))^n)/2), n=0..20); # _G. C. Greubel_, Jan 11 2020
%t Table[Round[((n+Sqrt[2])^n + (n-Sqrt[2])^n)/2], {n,0,20}] (* _G. C. Greubel_, Jan 11 2020 *)
%o (PARI) vector(21, n, round(((n-1-sqrt(2))^(n-1) + (n-1+sqrt(2))^(n-1))/2) ) \\ _G. C. Greubel_, Jan 11 2020
%o (Magma) [Round(((n-Sqrt(2))^n + (n+Sqrt(2))^n)/2): n in [0..20]]; // _G. C. Greubel_, Jan 11 2020
%o (Sage) [round(((n-sqrt(2))^n + (n+sqrt(2))^n)/2) for n in (0..20)] # _G. C. Greubel_, Jan 11 2020
%o (GAP) List([0..20], n-> ((n-Sqrt(2))^n + (n+Sqrt(2))^n)/2); # _G. C. Greubel_, Jan 11 2020
%Y Cf. A000312, A062024, A084061, A084062, A084063, A084065, A084095, A084096.
%K nonn,easy
%O 0,3
%A _Paul Barry_, May 11 2003
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