A099767 Number of n-digit palindromes in base n.

1, 6, 12, 100, 180, 2058, 3584, 52488, 90000, 1610510, 2737152, 57921708, 97883968, 2392031250, 4026531840, 111612119056, 187339329792, 5808378560022, 9728000000000, 333597619564020, 557758378619904, 20961814674106394, 34998666292887552, 1430511474609375000

Offset

2,2

Links

G. C. Greubel, Table of n, a(n) for n = 2..700

Formula

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

Example

a(3) = 6 because there are 6 3-digit palindromes in base 3, namely 101, 111, 121, 202, 212, 222.

Maple

seq((n-1)*n^(floor((n+1)/2) -1), n=2..30); # G. C. Greubel, Sep 03 2019

Mathematica

(n-1)*n^(Floor[(n+1)/2] -1) /. n -> Range[2, 30]

Prog

(PARI) vector(30, n, n*(n+1)^((n+2)\2 -1) ) \\ G. C. Greubel, Sep 03 2019
(Magma) [(n-1)*n^(Floor((n+1)/2) - 1): n in [2..30]]; // G. C. Greubel, Sep 03 2019
(SageMath) [(n-1)*n^(floor((n+1)/2) - 1) for n in (2..30)] # G. C. Greubel, Sep 03 2019
(GAP) List([2..30], n-> (n-1)*n^(Int((n+1)/2) - 1)); # G. C. Greubel, Sep 03 2019

Crossrefs

Sequence in context: A002898 A382772 A003613 * A191462 A340060 A080450

Adjacent sequences: A099764 A099765 A099766 * A099768 A099769 A099770

Keyword

easy,nonn,base

Author

Anonymous, Nov 11 2004

Extensions

Terms a(21) onward added by G. C. Greubel, Sep 03 2019

Status

approved