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A253146 A fractal tree, read by rows: for n > 2, T(n,1) = T(n-1,1)+2, T(n,n) = T(n-1,1)+3, and for k=2..n-1, T(n,k) = T(n-2,k-1). 4
1, 2, 3, 4, 1, 5, 6, 2, 3, 7, 8, 4, 1, 5, 9, 10, 6, 2, 3, 7, 11, 12, 8, 4, 1, 5, 9, 13, 14, 10, 6, 2, 3, 7, 11, 15, 16, 12, 8, 4, 1, 5, 9, 13, 17, 18, 14, 10, 6, 2, 3, 7, 11, 15, 19, 20, 16, 12, 8, 4, 1, 5, 9, 13, 17, 21, 22, 18, 14, 10, 6, 2, 3, 7, 11, 15 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It appears that:

1) partial sums of terms, situated on the outer leftmost leftwise triangle diagonal are equal to A002061(k), k>=1;

2) partial sums of terms, situated on the second (from the left) leftwise triangle diagonal represent recurrence a(k+1) = ((k-1)*a(k))/(k-3)-(2*(k+3))/(k-3), k>=3

3) partial sums of terms, situated on the outer rightmost rightwise triangle diagonal are equal to A000290(k)=k^2, k>=1. - Alexander R. Povolotsky, Dec 28 2014

LINKS

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Éric Angelini, A fractal tree, SeqFan list, Dec 27 2014.

EXAMPLE

.   1:                         1

.   2:                       2   3

.   3:                     4   1   5

.   4:                   6   2   3   7

.   5:                 8   4   1   5   9

.   6:              10   6   2   3   7  11

.   7:            12   8   4   1   5   9  13

.   8:          14  10   6   2   3   7  11  15

.   9:        16  12   8   4   1   5   9  13  17

.  10:      18  14  10   6   2   3   7  11  15  19

.  11:    20  16  12   8   4   1   5   9  13  17  21

.  12:  22  18  14  10   6   2   3   7  11  15  19  23 .

Removing the first and last entries from each row gives the same tree back again.

From N. J. A. Sloane, Jan 04 2015: (Start)

Eric Angelini's original posting to the Sequence Fans mailing list gave a different sequence, as follows:

..................................1,

.................................2,3,

................................4,1,5,

...............................6,2,3,7,

..................................8,

..............................9,4,1,5,10,

............................11,6,2,3,7,12,

................................13,14,

...............................15,8,16,

...........................17,9,4,1,5,10,18,

.........................19,11,6,2,3,7,12,20,

........................21,13,8,4,1,5,9,14,22,

.............................23,15,16,24,

.................................25,

...........................26,17,10,18,27,

......................28,19,11,6,2,3,7,12,20,29,

.....................30,21,13,8,4,1,5,9,14,22,31,

..........................32,23,15,16,24,33,

................................34,35,

..............................36,25,37,

........................38,26,17,10,18,27,39,

...................40,28,19,11,6,2,3,7,12,20,29,41,

..................42,30,21,13,8,4,1,5,9,14,22,31,43,

................44,32,23,15,10,6,2,3,7,11,16,24,33,45,

...............46,34,25,17,12,8,4,1,5,9,13,18,26,35,47,

.......................48,36,27,19,20,28,37,49,

.............50,38,29,21,14,10,6,2,3,7,11,15,22,30,39,51,

............52,40,31,23,16,12,8,4,1,5,9,13,17,24,32,41,53,

.....................54,42,33,25,18,26,34,43,55,

.............................56,44,45,57,

.................................58,

.....................................

The idea is that the n-th term is equal to the number of terms in the n-th row of the tree. This lovely sequence (whose precise definition is not clear to me) is not yet in the OEIS. (End)

The sequence referred to is A253028. - Felix Fröhlich, May 23 2016

PROG

(Haskell)

a253146 n k = a253146_tabl !! (n-1) !! (k-1)

a253146_row n = a253146_tabl !! (n-1)

a253146_tabl = [1] : [2, 3] : f [1] [2, 3] where

   f us vs@(v:_) = ws : f vs ws where

                   ws = [v + 2] ++ us ++ [v + 3]

CROSSREFS

Cf. A253028. Row sums appear to be A035608.

Sequence in context: A071437 A243713 A129709 * A253028 A133108 A055441

Adjacent sequences:  A253143 A253144 A253145 * A253147 A253148 A253149

KEYWORD

nonn,tabl

AUTHOR

Eric Angelini and Reinhard Zumkeller, Dec 27 2014

STATUS

approved

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Last modified August 22 16:17 EDT 2019. Contains 326178 sequences. (Running on oeis4.)