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A136175 Tribonacci array, T(n,k). 10
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

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)

LINKS

Table of n, a(n) for n=1..62.

FORMULA

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.)

EXAMPLE

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

CROSSREFS

Cf. A035513.

Sequence in context: A175004 A191734 A191443 * A129258 A256988 A104650

Adjacent sequences:  A136172 A136173 A136174 * A136176 A136177 A136178

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 18 2007

STATUS

approved

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Last modified June 24 00:11 EDT 2021. Contains 345403 sequences. (Running on oeis4.)