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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 December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)