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, 975297243746681101290583, 54893054306119586385788959

Offset

0,3

Links

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

Formula

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

a(n) ~ exp(n^(1/2) - 1/2 + 5/(6*n^(1/2)) - 3/(4*n) + 23/(40*n^(3/2))) * n^n / 2. - Amiram Eldar, Feb 09 2026

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 *)

Prog

(PARI) vector(21, n, round(((n-1-sqrt(n))^(n-1) + (n-1+sqrt(n))^(n-1))/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
(SageMath) [round(((n-sqrt(n+1))^n + (n+sqrt(n+1))^n)/2) for n in (0..20)] # G. C. Greubel, Jan 09 2020
(GAP) List([0..20], n-> ((n-Sqrt(n+1))^n + (n+Sqrt(n+1))^n)/2); # G. C. Greubel, Jan 09 2020

Crossrefs

Cf. A084061, A084062, A084095.

Sequence in context: A049464 A229078 A346683 * A184141 A380155 A349720

Adjacent sequences: A084060 A084061 A084062 * A084064 A084065 A084066

Keyword

easy,nonn

Author

Paul Barry, May 11 2003

Status

approved