A104968 Absolute row sums of triangle A104967.

1, 2, 4, 6, 6, 12, 22, 32, 34, 52, 100, 150, 170, 266, 438, 640, 766, 1196, 1996, 2888, 3210, 4994, 8534, 12392, 15106, 22154, 34366, 52134, 62148, 96956, 156396, 217416, 262062, 394164, 643908, 950944, 1150368, 1689176, 2600992, 3767888, 4840338

Offset: 0

Author

Paul D. Hanna, Mar 30 2005

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A104967, A104969.

Programs

Mathematica

A104967[n_, k_]:= A104967[n, k]= Sum[(-2)^j*Binomial[k+1, j]*Binomial[n-j, k], {j, 0, n-k}];
A104968[n_]:= A104968[n]= Sum[Abs[A104967[n, k]], {k,0,n}];
Table[A104968[n], {n, 0, 50}] (* G. C. Greubel, Jun 09 2021 *)

PARI

{a(n)=local(X=x+x*O(x^n)); sum(k=0,n,abs(polcoeff(polcoeff((1-2*X)/(1-X-X*y*(1-2*X)),n,x),k,y)))}

Sage

@cached_function
def A104967(n,k): return sum( (-2)^j*binomial(k+1,j)*binomial(n-j,k) for j in (0..n-k))
def A104968(n): return sum( abs(A104967(n,k)) for k in (0..n))
[A104968(n) for n in (0..50)] # G. C. Greubel, Jun 09 2021

Formula

a(n) = Sum_{k=0..n} abs(A104967(n,k)).