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A137680 Triangle read by rows, T(n,k) = T(n-1, k-1) - T(n-k, k-1); with leftmost term in each row = sum of all previous terms. 3
1, 1, 1, 3, 0, 1, 7, 2, 0, 1, 17, 4, 1, 0, 1, 40, 10, 4, 1, 0, 1, 96, 23, 8, 3, 1, 0, 1, 228, 56, 19, 8, 3, 1, 0, 1, 544, 132, 46, 18, 7, 3, 1, 0, 1, 1296, 316, 109, 42, 18, 7, 3, 1, 0, 1, 3089, 752, 260, 101, 41, 17, 7, 3, 1, 0, 1, 7361, 1793, 620, 241, 98, 41, 17, 7, 3, 1, 0, 1, 17544 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A variation of the same sequence = column 2 of the triangle: (1, 0, 2, 4, 10, 23, 56, 132,...) = first difference row of column 1. Left border of the triangle = A137682.

Left column starting (1, 3,...) = INVERT transform of A160096. [From Gary W. Adamson, May 01 2009]

LINKS

Table of n, a(n) for n=1..79.

EXAMPLE

First few rows of the triangle are:

1;

1, 1;

3, 0, 1;

7, 2, 0, 1;

17, 4, 1, 0, 1;

40, 10, 4, 1, 0, 1;

96, 23, 8, 3, 1, 0, 1;

228, 56, 19, 8, 3, 1, 0, 1;

544, 132, 46, 18, 7, 3, 1, 0, 1;

1296, 316, 109, 42, 18, 7, 3, 1, 0, 1;

3089, 752, 260, 101, 41, 17, 7, 3, 1, 0, 1;

...

MAPLE

A137680 := proc(n, k)

    if k < 1 or k > n then

        0 ;

    elif n = 1 then

        1;

    elif k = 1 then

        add(add(procname(r, j), j=1..r), r=1..n-1) ;

    else

        procname(n-1, k-1)-procname(n-k, k-1) ;

    end if;

end proc: # R. J. Mathar, Aug 12 2012

CROSSREFS

Cf. A137681 (row sums), A137682.

A160096 [From Gary W. Adamson, May 01 2009]

Sequence in context: A297786 A214407 A298668 * A248722 A201663 A199606

Adjacent sequences:  A137677 A137678 A137679 * A137681 A137682 A137683

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Feb 05 2008

STATUS

approved

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Last modified July 17 17:14 EDT 2019. Contains 325107 sequences. (Running on oeis4.)