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A099557 Slanted Pascal's triangle, read by rows, such that T(n,k) = binomial(n-[k/2],k) for [n*2/3]>=k>=0, where [x]=floor(x). 2
1, 1, 1, 1, 2, 0, 1, 3, 1, 0, 1, 4, 3, 1, 0, 1, 5, 6, 4, 0, 0, 1, 6, 10, 10, 1, 0, 0, 1, 7, 15, 20, 5, 1, 0, 0, 1, 8, 21, 35, 15, 6, 0, 0, 0, 1, 9, 28, 56, 35, 21, 1, 0, 0, 0, 1, 10, 36, 84, 70, 56, 7, 1, 0, 0, 0, 1, 11, 45, 120, 126, 126, 28, 8, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums form A005314. Antidiagonal sums form A099558.

LINKS

Table of n, a(n) for n=0..77.

FORMULA

G.f.: (1-x+x*y)/((1-x)^2-x^3*y^2).

EXAMPLE

Rows begin:

[1],

[1,1],

[1,2,0],

[1,3,1,0],

[1,4,3,1,0],

[1,5,6,4,0,0],

[1,6,10,10,1,0,0],

[1,7,15,20,5,1,0,0],

[1,8,21,35,15,6,0,0,0],

[1,9,28,56,35,21,1,0,0,0],

[1,10,36,84,70,56,7,1,0,0,0],...

and can be derived from Pascal's triangle

by shifting each column k down by [k/2] rows.

PROG

(PARI) {T(n, k)=polcoeff(polcoeff((1-x+x*y)/((1-x)^2-x^3*y^2)+x*O(x^n), n, x)+y*O(y^k), k, y)}

CROSSREFS

Cf. A005314, A099558.

Sequence in context: A174067 A124943 A169803 * A214576 A079217 A079221

Adjacent sequences:  A099554 A099555 A099556 * A099558 A099559 A099560

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Oct 22 2004

STATUS

approved

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Last modified April 8 12:16 EDT 2020. Contains 333314 sequences. (Running on oeis4.)