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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. 14
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_{i=0..n-1} (k+1)^i.

T(n,k) = A055129(n,k+1) = A104878(n+k,k+1), 1<=k<=n. - Mathew Englander, Dec 19 2020

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

This triangle shares some features with triangle A104878.

This triangle is a portion of rectangle A055129.

Each term of A110737 comes from the corresponding row of this triangle.

Diagonals (adjusting offset as necessary): A060072, A023037, A031973, A173468.

Columns (adjusting offset as necessary): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724, A218725, A218726, A218727, A218728, A218729, A218730, A218731, A218732, A218733, A218734, A132469, A218736, A218737, A218738, A218739, A218740, A218741, A218742, A218743, A218744, A218745, A218746, A218747, A218748, A218749, A218750, A218751, A218753, A218752.

Sequence in context: A193883 A227038 A189994 * A310008 A299024 A116201

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 March 9 03:35 EST 2021. Contains 341962 sequences. (Running on oeis4.)