A030111 Triangular array in which k-th entry in n-th row is C([ (n+k)/2 ],k) (1<=k<=n).

1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 3, 4, 1, 1, 3, 6, 4, 5, 1, 1, 4, 6, 10, 5, 6, 1, 1, 4, 10, 10, 15, 6, 7, 1, 1, 5, 10, 20, 15, 21, 7, 8, 1, 1, 5, 15, 20, 35, 21, 28, 8, 9, 1, 1, 6, 15, 35, 35, 56, 28, 36, 9, 10, 1, 1, 6, 21, 35, 70, 56, 84, 36, 45, 10, 11, 1, 1, 7, 21, 56, 70, 126, 84, 120, 45, 55, 11, 12, 1

Offset: 1

Author

Jacques Haubrich (jhaubrich(AT)freeler.nl)

Keywords

• tabl
• nonn

Comments

Same as A046854, but missing the initial column of ones.

Riordan array (1/((1-x)(1-x^2)),x/(1-x^2)). Diagonal sums are A052551. - Paul Barry, Sep 30 2006

Examples

			1;
1 1;
2 1 1;
2 3 1 1;
3 3 4 1 1;
3 6 4 5 1 1;
...
		

Links

• Indranil Ghosh, Rows 0..125, flattened

Crossrefs

Cf. A066170.

Programs

Mathematica

Flatten[Table[Binomial[Floor[(n+k)/2],k],{n,20},{k,n}]] (* Harvey P. Dale, Jun 03 2014 *)

PARI

{T(n, k) = binomial((n+k)\2, k)}; /* Michael Somos, Jul 23 1999 */

PARI

printp(matrix(8,8,n,k,binomial((n+k)\2,k)))

PARI

for(n=1,7, for(k=1,n,print1(binomial((n+k)\2,k)); if(k==n,print1("; ")); print1(" ")))

Formula

G.f.: 1 / (1 - x - xy - x^2 + x^2y + x^3). - Ralf Stephan, Feb 13 2005

Sum(k=1, n, T(n, k)) = F(n+2)-1 where F(n) is the n-th Fibonacci number. - Benoit Cloitre, Oct 07 2002

Extensions

Description corrected by Michael Somos, Jul 23 1999

Corrected and extended by Harvey P. Dale, Jun 03 2014