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Search: id:A125118
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| A125118 |
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Triangle read by rows: T(n,k) = value of the n-th repunit in base (k+1) representation, 1<=k<=n. |
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+0
12
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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);
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LINKS
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Eric Weisstein's World of Mathematics, Repunit
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FORMULA
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T(n,k) = Sum((k+1)^i: 0<=i<n).
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EXAMPLE
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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
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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.
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CROSSREFS
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Sequence in context: A055664 A089374 A029552 this_sequence A116201 A092406 A121174
Adjacent sequences: A125115 A125116 A125117 this_sequence A125119 A125120 A125121
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KEYWORD
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nonn,tabl,base
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 21 2006
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