A152198 Triangle read by rows, A007318 rows repeated.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1

Offset

0,8

Comments

Eigensequence of the triangle = A051163: (1, 2, 5, 12, 30, 76,...)

Another version of A152815. - Philippe Deléham, Dec 13 2008

Row sums : A016116(n); Diagonal sums: A000931(n+5). - Philippe Deléham, Dec 13 2008

Triangle, with zeros omitted, given by (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 16 2012

Sums along rising diagonals are A134816. - John Molokach, Jul 09 2013

Links

Table of n, a(n) for n=0..89.

Formula

Triangle read by rows, Pascal's triangle rows repeated.

Equals inverse binomial transform of A133156 unsigned.

G.f. : (1+x)/(1-(1+y)*x^2). - Philippe Deléham, Jan 16 2012

Sum_{k, 0<=k<=n} T(n,k)*x^k = A057077(n), A019590(n+1), A000012(n), A016116(n), A108411(n), A074872(n+1) for x = -2, -1, 0, 1, 2, 4 respectively. - Philippe Deléham, Jan 16 2012

T(n,k) = A065941(n-k, n-2*k) = abs(A108299(n-k, n-2*k)). - Johannes W. Meijer, Sep 05 2013

Example

The triangle starts
1;
1;
1, 1;
1, 1;
1, 2, 1;
1, 2, 1;
1, 3, 3, 1;
1, 3, 3, 1;
1, 4, 6, 4, 1;
1, 4, 6, 4, 1;
1, 5, 10, 10, 5, 1;
1, 5, 10, 10, 5, 1;
...
Triangle (1,0,-1,0,0,...) DELTA (0,1,-1,0,0,...) begins:
1
1, 0
1, 1, 0
1, 1, 0, 0
1, 2, 1, 0, 0
1, 2, 1, 0, 0, 0
1, 3, 3, 1, 0, 0, 0
1, 3, 3, 1, 0, 0, 0, 0
1, 4, 6, 4, 1, 0, 0, 0, 0
1, 4, 6, 4, 1, 0, 0, 0, 0, 0
1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0...

Mathematica

t[n_, k_] := Binomial[ Floor[n/2], k]; Table[t[n, k], {n, 0, 17}, {k, 0, Floor[n/2]}] // Flatten (* Jean-François Alcover, Sep 13 2012 *)

Crossrefs

Cf. A007318, A133156, A051163.

Sequence in context: A161042 A029292 A343662 * A259342 A258280 A159255

Adjacent sequences: A152195 A152196 A152197 * A152199 A152200 A152201

Keyword

nonn,tabf

Author

Gary W. Adamson, Nov 28 2008

Extensions

More terms from Philippe Deléham, Dec 14 2008

Status

approved