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A055129 Repunits in different bases: table by antidiagonals of numbers written in base k as a string of n 1's. 7
1, 1, 2, 1, 3, 3, 1, 4, 7, 4, 1, 5, 13, 15, 5, 1, 6, 21, 40, 31, 6, 1, 7, 31, 85, 121, 63, 7, 1, 8, 43, 156, 341, 364, 127, 8, 1, 9, 57, 259, 781, 1365, 1093, 255, 9, 1, 10, 73, 400, 1555, 3906, 5461, 3280, 511, 10, 1, 11, 91, 585, 2801, 9331, 19531, 21845, 9841, 1023, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (1 <= n <= 150).

FORMULA

T(n, k) = (k^n-1)/(k-1) [with T(n, 1) = n] = T(n-1, k)+k^(n-1) = (k+1)*T(n-1, k)-k*T(n-2, k) [with T(0, k) = 0 and T(1, k) = 1].

EXAMPLE

T(3,5)=31 because 111 base 5 represents 25+5+1=31.

      1       1       1       1       1       1       1

      2       3       4       5       6       7       8

      3       7      13      21      31      43      57

      4      15      40      85     156     259     400

      5      31     121     341     781    1555    2801

      6      63     364    1365    3906    9331   19608

      7     127    1093    5461   19531   55987  137257

MAPLE

A055129 := proc(n, k)

    add(k^j, j=0..n-1) ;

end proc: # R. J. Mathar, Dec 09 2015

MATHEMATICA

Table[FromDigits[ConstantArray[1, #], k] &[n - k + 1], {n, 11}, {k, n, 1, -1}] // Flatten (* or *)

Table[If[k == 1, n, (k^# - 1)/(k - 1) &[n - k + 1]], {n, 11}, {k, n, 1, -1}] // Flatten (* Michael De Vlieger, Dec 11 2016 *)

CROSSREFS

Rows include A000012, A000027, A002061, A053698, A053699, A053700. Columns (see recurrence) include A000027, A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002275, A016123, A016125. Diagonals include A023037, A031973. Numbers in the table (apart form first column and first two rows) are ordered in A053696.

Sequence in context: A098546 A126277 A253273 * A133804 A185943 A208337

Adjacent sequences:  A055126 A055127 A055128 * A055130 A055131 A055132

KEYWORD

base,easy,nonn,tabl

AUTHOR

Henry Bottomley, Jun 14 2000

STATUS

approved

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Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.)