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A089178 Triangle T(n,k) (n >= 0, 0 <= k <= 1+log_2(floor(n+1)) read by rows: row 0 = {1}, row 1 = {1 1}; for n >=2, row n = row n-1 + (row floor((n-1)/2) shifted one place right). 2
1, 1, 1, 1, 2, 1, 3, 1, 1, 4, 2, 1, 5, 4, 1, 6, 6, 1, 7, 9, 1, 1, 8, 12, 2, 1, 9, 16, 4, 1, 10, 20, 6, 1, 11, 25, 10, 1, 12, 30, 14, 1, 13, 36, 20, 1, 14, 42, 26, 1, 15, 49, 35, 1, 1, 16, 56, 44, 2, 1, 17, 64, 56, 4, 1, 18, 72, 68, 6, 1, 19, 81, 84, 10, 1, 20, 90, 100, 14, 1, 21, 100, 120, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Rows n = 0..1094, flattened

N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.

FORMULA

G.f.: (1/(1-x))*(1+Sum(y^(k+1)*x^(2^(k+1)-1)/Product(1-x^(2^j), j=0..k), k=0..infinity)).

EXAMPLE

Triangle begins:

1;

1, 1;

1, 2;

1, 3, 1;

1, 4, 2;

1, 5, 4;

1, 6, 6;

1, 7, 9, 1;

MAPLE

T:= proc(n) option remember; `if`(n=0, 1,

      zip((x, y)-> x+y, [T(n-1)], [0, T(floor((n-1)/2))], 0)[])

    end:

seq(T(n), n=0..25);  # Alois P. Heinz, Apr 01 2012

MATHEMATICA

row[0] = {1}; row[n_] := row[n] = PadRight[{row[n-1], Join[{0}, row[Floor[(n-1)/2]]]}] // Total; Table[row[n], {n, 0, 25}] // Flatten (* Jean-Fran├žois Alcover, Nov 27 2014 *)

CROSSREFS

Also obtained by dividing rows of A089177 by "1 1".

Row sums give A033485.

Sequence in context: A210992 A220484 A174066 * A187489 A116599 A138121

Adjacent sequences:  A089175 A089176 A089177 * A089179 A089180 A089181

KEYWORD

nonn,tabf,easy

AUTHOR

N. J. A. Sloane, Dec 08 2003

EXTENSIONS

More terms from Vladeta Jovovic, Dec 10 2003

STATUS

approved

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Last modified January 26 23:54 EST 2022. Contains 350601 sequences. (Running on oeis4.)