A084063 First subdiagonal of number array A084061.

1, 1, 7, 63, 761, 11525, 209539, 4440527, 107374753, 2915352729, 87771145551, 2900744369039, 104369641697881, 4060189444664093, 169777979925475531, 7592652139022106975, 361563242499379729537, 18263719440778358953457

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, A084095.

Programs

GAP

List([0..20], n-> ((n-Sqrt(n+1))^n + (n+Sqrt(n+1))^n)/2); # G. C. Greubel, Jan 09 2020

Magma

[Round(((n-Sqrt(n+1))^n + (n+Sqrt(n+1))^n)/2): n in [0..20]]; // G. C. Greubel, Jan 09 2020

Maple

seq( round(((n-sqrt(n+1))^n + (n+sqrt(n+1))^n)/2), n=0..20); # G. C. Greubel, Jan 09 2020

Mathematica

Table[Round[((n+Sqrt[n+1])^n + (n-Sqrt[n+1])^n)/2], {n,0,20}] (* G. C. Greubel, Jan 09 2020 *)

PARI

vector(21, n, round(((n-1-sqrt(n))^(n-1) + (n-1+sqrt(n))^(n-1))/2) ) \\ G. C. Greubel, Jan 09 2020

Sage

[round(((n-sqrt(n+1))^n + (n+sqrt(n+1))^n)/2) for n in (0..20)] # G. C. Greubel, Jan 09 2020

Formula

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