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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. 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) LINKS 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 A104650 A083179 Adjacent sequences:  A136172 A136173 A136174 * A136176 A136177 A136178 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 18 2007 STATUS approved

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