0,14

Triangle inverse has general term (-1)^(n-k)*binomial(floor(n/2),n-k)}. Diagonal sums are A103632.

Triangle T(n,k), 0<=k<=n, rad by rows, given by [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 08 2005

Row sums are Fibonacci numbers (A000045).

Another version of triangle in A065941 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 01 2009]

Number triangle T(n, k)=binomial(floor((2n-k-1)/2), n-k)

Sum_{k, 0<=k<=n}T(n,k)*x^k = A152163(n), A000007(n), A000045(n+1), A026597(n), A122994(n+1), A158608(n), A122995(n+1), A158797(n), A122996(n+1), A158798(n), A158609(n) for x = -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 12 2009]

Rows begin {1}, {0,1}, {0,1,1}, {0,1,1,1}, {0,1,1,2,1},..

Contribution from Paul Barry (pbarry(AT)wit.ie), Oct 02 2009: (Start)

Triangle begins

1,

0, 1,

0, 1, 1,

0, 1, 1, 1,

0, 1, 1, 2, 1,

0, 1, 1, 3, 2, 1,

0, 1, 1, 4, 3, 3, 1,

0, 1, 1, 5, 4, 6, 3, 1,

0, 1, 1, 6, 5, 10, 6, 4, 1,

0, 1, 1, 7, 6, 15, 10, 10, 4, 1

Production matrix is

0, 1,

0, 1, 1,

0, 0, 0, 1,

0, 0, 0, 1, 1,

0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 1, 1,

0, 0, 0, 0, 0, 0, 0, 1,

0, 0, 0, 0, 0, 0, 0, 1, 1,

0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (End)

A polynomial recursion which produces this triangle: p(x, n) = p(x, n - 1) + x^2*p(x, n - 2). - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008

p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x; p[x, 2] = x + x^2; p[x_, n_] := p[x, n] = p[x, n - 1] + x^2*p[x, n - 2]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008

Cf. A103633.

Sequence in context: A137560 A131255 A133607 this_sequence A083856 A081718 A129634

Adjacent sequences: A103628 A103629 A103630 this_sequence A103632 A103633 A103634

easy,nonn,tabl

Paul Barry (pbarry(AT)wit.ie), Feb 11 2005