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A125118 Triangle read by rows: T(n,k) = value of the n-th repunit in base (k+1) representation, 1<=k<=n. 11
1, 3, 4, 7, 13, 21, 15, 40, 85, 156, 31, 121, 341, 781, 1555, 63, 364, 1365, 3906, 9331, 19608, 127, 1093, 5461, 19531, 55987, 137257, 299593, 255, 3280, 21845, 97656, 335923, 960800, 2396745, 5380840, 511, 9841, 87381, 488281, 2015539, 6725601 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

T(n+1,k) = (k+1)*T(n,k) + 1;

row sums give A125120; central terms give A125119;

T(n,1) = A000225(n);

T(n,2) = A003462(n) for n>1;

T(n,3) = A002450(n) for n>2;

T(n,4) = A003463(n) for n>3;

T(n,5) = A003464(n) for n>4;

T(n,9) = A002275(n) for n>8;

T(n,n-2) = A031973(n) for n>2;

T(n,n-1) = A023037(n) for n>1;

T(n,n) = A060072(n+1);

LINKS

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Repunit

FORMULA

T(n,k) = Sum((k+1)^i: 0<=i<n).

EXAMPLE

First 4 rows:

1: [1]_2

2: [11]_2 ........ [11]_3

3: [111]_2 ....... [111]_3 ....... [111]_4

4: [1111]_2 ...... [1111]_3 ...... [1111]_4 ...... [1111]_5

_

1: 1

2: 2+1 ........... 3+1

3: (2+1)*2+1 ..... (3+1)*3+1 ..... (4+1)*4+1

4: ((2+1)*2+1)*2+1 ((3+1)*3+1)*3+1 ((4+1)*4+1)*4+1

((5+1)*5+1)*5+1.

CROSSREFS

Sequence in context: A193883 A227038 A189994 * A116201 A280224 A282718

Adjacent sequences:  A125115 A125116 A125117 * A125119 A125120 A125121

KEYWORD

nonn,tabl,base

AUTHOR

Reinhard Zumkeller, Nov 21 2006

STATUS

approved

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Last modified July 27 04:25 EDT 2017. Contains 289841 sequences.