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A187081 Triangle T(n,k) read by rows: sand piles of n grains and height k. 1
1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0, 0, 1, 7, 0, 0, 0, 0, 0, 0, 1, 12, 0, 0, 0, 0, 0, 0, 0, 1, 20, 1, 0, 0, 0, 0, 0, 0, 0, 1, 33, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 54, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 88, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 143, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 232, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 376, 84, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,18

COMMENTS

See A186085 for the definition of sand piles.

LINKS

Table of n, a(n) for n=0..125.

FORMULA

For n>=2 we have T(n,1)+T(n,2) = Fibonacci(n-1).

T(n,2) = A000071(n). [Joerg Arndt, Sep 17 2013]

EXAMPLE

Triangle begins:

1;

0,1;

0,1,0;

0,1,0,0;

0,1,1,0,0;

0,1,2,0,0,0;

0,1,4,0,0,0,0;

0,1,7,0,0,0,0,0;

0,1,12,0,0,0,0,0,0;

0,1,20,1,0,0,0,0,0,0;

0,1,33,2,0,0,0,0,0,0,0;

0,1,54,5,0,0,0,0,0,0,0,0;

0,1,88,11,0,0,0,0,0,0,0,0,0;

0,1,143,22,0,0,0,0,0,0,0,0,0,0;

0,1,232,44,0,0,0,0,0,0,0,0,0,0,0;

0,1,376,84,0,0,0,0,0,0,0,0,0,0,0,0;

0,1,609,158,1,0,0,0,0,0,0,0,0,0,0,0,0;

0,1,986,293,2,0,0,0,0,0,0,0,0,0,0,0,0,0;

0,1,1596,535,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0;

0,1,2583,969,12,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;

0,1,4180,1739,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;

0,1,6764,3099,52,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;

0,1,10945,5491,103,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;

The 22 compositions corresponding to sand piles of 9 grains are the following:

    #:    composition              height

    1:    [ 1 2 3 2 1 ]              3

    2:    [ 1 2 2 2 1 1 ]            2

    3:    [ 1 2 2 1 2 1 ]            2

    4:    [ 1 2 1 2 2 1 ]            2

    5:    [ 1 1 2 2 2 1 ]            2

    6:    [ 1 2 2 1 1 1 1 ]          2

    7:    [ 1 2 1 2 1 1 1 ]          2

    8:    [ 1 1 2 2 1 1 1 ]          2

    9:    [ 1 2 1 1 2 1 1 ]          2

   10:    [ 1 1 2 1 2 1 1 ]          2

   11:    [ 1 1 1 2 2 1 1 ]          2

   12:    [ 1 2 1 1 1 2 1 ]          2

   13:    [ 1 1 2 1 1 2 1 ]          2

   14:    [ 1 1 1 2 1 2 1 ]          2

   15:    [ 1 1 1 1 2 2 1 ]          2

   16:    [ 1 2 1 1 1 1 1 1 ]        2

   17:    [ 1 1 2 1 1 1 1 1 ]        2

   18:    [ 1 1 1 2 1 1 1 1 ]        2

   19:    [ 1 1 1 1 2 1 1 1 ]        2

   20:    [ 1 1 1 1 1 2 1 1 ]        2

   21:    [ 1 1 1 1 1 1 2 1 ]        2

   22:    [ 1 1 1 1 1 1 1 1 1 ]      1

  stats:  0 1 20 1 0 0 0 0 0 0

CROSSREFS

Row sums are A186085 (sand piles of n grains), cf. A186084 (sand piles by base length), A047998 (fountains of coins by base length).

Sequence in context: A039968 A092037 A166301 * A212434 A227186 A037134

Adjacent sequences:  A187078 A187079 A187080 * A187082 A187083 A187084

KEYWORD

nonn,tabl

AUTHOR

Joerg Arndt, Mar 08 2011

STATUS

approved

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Last modified November 18 17:56 EST 2017. Contains 294894 sequences.