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A337277 Stern's triangle read by rows. 5
1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 3, 2, 3, 1, 3, 2, 3, 1, 2, 1, 1, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

The first two rows are 1, then 1,1,1. To get row n, copy row n-1, and insert c+d between every pair of adjacent terms c,d, and finally insert a 1 at the beginning and end of the row.

The maximum value in row n is A000045(n+1). - Alois P. Heinz, Sep 09 2020

REFERENCES

Stanley, Richard P. "Some Linear Recurrences Motivated by Stern’s Diatomic Array." The American Mathematical Monthly 127.2 (2020): 99-111.

LINKS

Alois P. Heinz, Rows n = 0..14, flattened

Richard P. Stanley, Some Linear Recurrences Motivated by Stern's Diatomic Array, arXiv:1901.04647 [math.CO], 2019.

FORMULA

T(n,n) = A002487(n+1). - Alois P. Heinz, Sep 09 2020

EXAMPLE

Triangle begins:

  1;

  1, 1, 1;

  1, 1, 2, 1, 2, 1, 1;

  1, 1, 2, 1, 3, 2, 3, 1, 3, 2, 3, 1, 2, 1, 1;

  1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1;

  ...

MAPLE

T:= proc(n) option remember; `if`(n=0, 1, (L-> [1, L[1], seq(

      [L[i-1]+L[i], L[i]][], i=2..nops(L)), 1][])([T(n-1)]))

    end:

seq(T(n), n=0..6);  # Alois P. Heinz, Sep 09 2020

MATHEMATICA

Nest[Append[#, Flatten@ Join[{1}, If[Length@ # > 1, Map[{#1, #1 + #2} & @@ # &, Partition[#[[-1]], 2, 1] ], {}], {#[[-1, -1]]}, {1}]] &, {{1}}, 5] // Flatten (* Michael De Vlieger, Sep 09 2020 *)

CROSSREFS

Cf. A000045, A002487, A049456, A334627.

Row sums give A000244.

Row lengths give A126646.

Sequence in context: A103414 A092400 A303598 * A269974 A269975 A308069

Adjacent sequences:  A337274 A337275 A337276 * A337278 A337279 A337280

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Sep 09 2020

STATUS

approved

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Last modified January 15 19:15 EST 2021. Contains 340189 sequences. (Running on oeis4.)