A030111 - OEIS

%I #28 Feb 19 2017 03:30:23

%S 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,

%T 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,

%U 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

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

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

%C Riordan array (1/((1-x)(1-x^2)),x/(1-x^2)). Diagonal sums are A052551. - _Paul Barry_, Sep 30 2006

%H Indranil Ghosh, <a href="/A030111/b030111.txt">Rows 0..125, flattened</a>

%F G.f.: 1 / (1 - x - xy - x^2 + x^2y + x^3). - _Ralf Stephan_, Feb 13 2005

%F 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

%e 1;

%e 1 1;

%e 2 1 1;

%e 2 3 1 1;

%e 3 3 4 1 1;

%e 3 6 4 5 1 1;

%e ...

%t Flatten[Table[Binomial[Floor[(n+k)/2],k],{n,20},{k,n}]] (* _Harvey P. Dale_, Jun 03 2014 *)

%o (PARI) {T(n, k) = binomial((n+k)\2, k)}; /* _Michael Somos_, Jul 23 1999 */

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

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

%Y Cf. A066170.

%K tabl,nonn

%O 1,4

%A Jacques Haubrich (jhaubrich(AT)freeler.nl)

%E Description corrected by _Michael Somos_, Jul 23 1999

%E Corrected and extended by _Harvey P. Dale_, Jun 03 2014