OFFSET
1,2
COMMENTS
Eric Angelini's original posting to the Sequence Fans mailing list gave a similar but different lovely sequence, which is now A253028. - N. J. A. Sloane, Jan 04 2015, and Felix Fröhlich, May 23 2016
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.
MATHEMATICA
T[n_, 1] := 2n - 2;
T[n_, n_] := 2n - 1;
T[n_, k_] := T[n, k] = T[n-2, k-1];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 20 2021 *)
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
KEYWORD
nonn,tabl
AUTHOR
Eric Angelini and Reinhard Zumkeller, Dec 27 2014
STATUS
approved