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A099573
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Reverse of number triangle A054450.
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1
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1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 4, 5, 1, 1, 5, 5, 8, 8, 1, 1, 6, 6, 12, 12, 13, 1, 1, 7, 7, 17, 17, 21, 21, 1, 1, 8, 8, 23, 23, 33, 33, 34, 1, 1, 9, 9, 30, 30, 50, 50, 55, 55, 1, 1, 10, 10, 38, 38, 73, 73, 88, 88, 89, 1, 1, 11, 11, 47, 47, 103, 103, 138, 138, 144, 144, 1, 1, 12, 12, 57
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Row sums are A029907(n+1). Diagonal sums are A099574. Diagonal is A000045(n+1).
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FORMULA
| Number triangle T(n, k)=if(k<=n, sum{j=0..floor(k/2), binomial(n-j, j)}, 0).
Antidiagonals of the following array: the first row equals the Fibonacci numbers, (1, 1, 2, 3, 5,...), and the (n+1)-st row is obtained by the matrix-vector product A128174 * n-th row. - Gary W. Adamson, Jan 19 2011
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EXAMPLE
| Rows of the triangle start {1}, {1,1}, {1,1,2}, {1,1,3,3}, {1,1,4,4,5},...
First few rows of the array are:
1, 1, 2, 3,. 5, .8,... A000045
1, 1, 3, 4,. 8, 12,... A052952
1, 1, 4, 5,.12, 17,... A054451
1, 1, 5, 6,.17, 23,... A099571
1, 1, 6, 7,.23, 30,... A099572
...
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CROSSREFS
| Cf. A099575, A054450.
Sequence in context: A049695 A096589 A176427 * A107430 A132892 A174448
Adjacent sequences: A099570 A099571 A099572 * A099574 A099575 A099576
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Oct 23 2004
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