A111568 -id:A111568

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A093460

a(n) = 2n^(n-1) - 1.

+10
6

1, 3, 17, 127, 1249, 15551, 235297, 4194303, 86093441, 1999999999, 51874849201, 1486016741375, 46596170244961, 1587429546508287, 58385852050781249, 2305843009213693951, 97322383751333736961, 4371823119477393063935

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(n) = A111568(n,n-1), i.e., diagonal of A111568. A111568 is the triangle whose n-th row contains n terms of the arithmetic progression having first term 1 and common difference 2*(n^(n-1)-1)/(n-1). - Emeric Deutsch, Aug 08 2005

LINKS

Table of n, a(n) for n=1..18.

MAPLE

a:=n->2*n^(n-1)-1: seq(a(n), n=1..20); # Emeric Deutsch, Aug 08 2005

MATHEMATICA

f[n_] := 2*n^(n-1) - 1; Table[f[i], {i, 1, 30}] (* Ryan Propper, Aug 08 2005 *)

CROSSREFS

Cf. A093461, A111568.

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Apr 05 2004

EXTENSIONS

More terms from Emeric Deutsch and Ryan Propper, Aug 08 2005

STATUS

approved

A093461

a(1)=1, a(n) = 2*(n^(n-1)-1)/(n-1) for n >= 2.

+10
3

1, 2, 8, 42, 312, 3110, 39216, 599186, 10761680, 222222222, 5187484920, 135092431034, 3883014187080, 122109965116022, 4170418003627232, 153722867280912930, 6082648984458358560, 257166065851611356702

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Proposition: n^(n-1) - 1 == 0 (mod (n-1)^2). Hence a(n) == 0 mod (n-1).

a(n) is the common difference of the arithmetic progression in row n of A111568. Written in base n, a(n) has n-1 digits equal to 2 (for example, a(10)=222222222). - Emeric Deutsch, Aug 08 2005

LINKS

Table of n, a(n) for n=1..18.

FORMULA

a(1) = 1, a(n) = 2*(n^(n-1) - 1)/(n-1) for n > 1.