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A136175
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Tribonacci array, T(n,k).
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10
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1, 2, 3, 4, 6, 5, 7, 11, 9, 8, 13, 20, 17, 15, 10, 24, 37, 36, 28, 19, 12, 44, 68, 57, 51, 35, 22, 14, 81, 125, 105, 94, 64, 41, 26, 16, 149, 230, 193, 173, 118, 75, 48, 30, 18, 274, 423, 355, 318, 217, 138, 88, 55, 33, 21, 504, 778, 653, 585, 399, 254, 162
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OFFSET
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1,2
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COMMENTS
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As an interspersion (and dispersion), the array is, as a sequence, a permutation of the positive integers. Column k consists of the numbers m such that the least summand in the tribonacci representation of m is T(1,k). For example, column 1 consists of numbers with least summand 1. This array arises from tribonacci representations in much the same way that the Wythoff array, A035513, arises from Fibonacci (or Zeckendorf) representations.
Comments from Abel Amene, Jul 29 2012: (Start)
(Row 1) = A000073 (offset=4) a(0)=0, a(1)=0, a(2)=1
(Row 2) = A001590 (offset=5) a(0)=0, a(1)=1, a(2)=0
(Row 3) = A001590 (offset=4) a(0)=1, a(1)=1, a(2)=1
(Row 4) = A214899 (offset=5) a(0)=2, a(1)=1, a(2)=2
(Row 5) = A020992 (offset=6) a(0)=0, a(1)=2, a(2)=1
(Row 6) = A100683 (offset=6) a(0)=-1,a(1)=2, a(2)=2
(Row 7) = A135491 (offset=4) a(0)=2, a(1)=4, a(2)=8
(Row 8) = A214727 (offset=6) a(0)=1, a(1)=1, a(2)=2
(Row 9) = A081172 (offset=8) a(0)=1, a(1)=1, a(2)=0
(column 1)= A003265
(End)
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LINKS
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Table of n, a(n) for n=1..62.
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FORMULA
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T(1,1)=1, T(1,2)=2, T(1,3)=4, T(1,k)=T(1,k-1)+T(1,k-2)+T(1,k-3) for k>3. Row 1 is the tribonacci basis; write B(k)=T(1,k). Each row satisfies the recurrence T(n,k)=T(n,k-1)+T(n,k-2)+T(n,k-3). T(n,1) is least number not in an earlier row. If T(n,1) has tribonacci representation B(k(1))+B(k(2))+...+B(k(m)), then T(n,2) = B(k(2))+B(k(3))+...+B(k(m+1)) and T(n,3) = B(k(3))+B(k(4))+...+B(k(m+2)). (Continued shifting of indices gives the other terms in row n, also.)
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EXAMPLE
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Northwest corner:
1 2 4 7 13 24 44 81 149 274 504
3 6 11 20 37 68 125 230 423 778
5 9 17 36 57 105 193 355 653
8 15 28 51 94 173 318 585
10 19 35 64 118 217 399
12 22 41 75 138 254
14 26 48 88 162
16 30 55
18 33
21
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CROSSREFS
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Cf. A035513.
Sequence in context: A175004 A191734 A191443 * A129258 A104650 A083179
Adjacent sequences: A136172 A136173 A136174 * A136176 A136177 A136178
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Dec 18 2007
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STATUS
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approved
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