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A187080 Triangle T(n,k) read by rows: fountains of n coins and height k. 2
1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 4, 0, 0, 0, 0, 1, 7, 1, 0, 0, 0, 0, 1, 12, 2, 0, 0, 0, 0, 0, 1, 20, 5, 0, 0, 0, 0, 0, 0, 1, 33, 11, 0, 0, 0, 0, 0, 0, 0, 1, 54, 22, 1, 0, 0, 0, 0, 0, 0, 0, 1, 88, 44, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 143, 85, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 232, 161, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 376, 302, 25, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

See A005169 for the definition of a "fountain of n coins".  [John W. Layman, Mar 10 2011]

LINKS

Seiichi Manyama, Rows n = 0..25, flattened

FORMULA

T(n,1)+T(n,2) = Fibonacci(n).

EXAMPLE

Triangle begins:

1;

0,1;

0,1,0;

0,1,1,0;

0,1,2,0,0;

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

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

0,1,12,2,0,0,0,0;

0,1,20,5,0,0,0,0,0;

0,1,33,11,0,0,0,0,0,0;

0,1,54,22,1,0,0,0,0,0,0;

0,1,88,44,2,0,0,0,0,0,0,0;

0,1,143,85,5,0,0,0,0,0,0,0,0;

0,1,232,161,12,0,0,0,0,0,0,0,0,0;

0,1,376,302,25,0,0,0,0,0,0,0,0,0,0;

0,1,609,559,52,1,0,0,0,0,0,0,0,0,0,0;

0,1,986,1026,105,2,0,0,0,0,0,0,0,0,0,0,0;

0,1,1596,1870,207,5,0,0,0,0,0,0,0,0,0,0,0,0;

The 15 compositions corresponding to fountains of 7 coins are the following:

   #:    composition      height

   1:    [ 1 2 3 1 ]        3

   2:    [ 1 2 2 2 ]        2

   3:    [ 1 1 2 3 ]        3

   4:    [ 1 2 2 1 1 ]      2

   5:    [ 1 2 1 2 1 ]      2

   6:    [ 1 1 2 2 1 ]      2

   7:    [ 1 2 1 1 2 ]      2

   8:    [ 1 1 2 1 2 ]      2

   9:    [ 1 1 1 2 2 ]      2

  10:    [ 1 2 1 1 1 1 ]    2

  11:    [ 1 1 2 1 1 1 ]    2

  12:    [ 1 1 1 2 1 1 ]    2

  13:    [ 1 1 1 1 2 1 ]    2

  14:    [ 1 1 1 1 1 2 ]    2

  15:    [ 1 1 1 1 1 1 1 ]  1

  stats:  0 1 12 2 0 0 0 0

CROSSREFS

Row sums give A005169 (fountains of n coins).

Cf. A047998, A187081 (sand piles by height).

Sequence in context: A227345 A123262 A191906 * A301342 A226369 A320751

Adjacent sequences:  A187077 A187078 A187079 * A187081 A187082 A187083

KEYWORD

nonn,tabl

AUTHOR

Joerg Arndt, Mar 08 2011

STATUS

approved

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Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)