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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 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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