A084613 a(n) = sum of absolute values of coefficients of (1 + x - 2*x^2)^n.

1, 4, 14, 44, 124, 394, 1418, 4706, 14322, 40712, 135878, 468934, 1513650, 4502864, 13421408, 45258442, 152708520, 483810550, 1413811358, 4483843328, 15051967962, 49724234652, 154802614364, 461020649750, 1486736569982

Offset: 0

Author

Paul D. Hanna, Jun 01 2003

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A002426, A084600 to A084612, A084614, A084615.

Programs

Magma

A084612:= func< n,k | (&+[Binomial(n, k-j)*Binomial(k-j, j)*(-2)^j: j in [0..k]]) >;
[(&+[Abs(A084612(n,k)): k in [0..2*n]]): n in [0..50]]; // G. C. Greubel, Mar 25 2023

Mathematica

Table[Total[Abs[CoefficientList[Expand[(1+x-2x^2)^n],x]]],{n,0,30}]  (* Harvey P. Dale, Apr 21 2011 *)

PARI

for(n=0,40,S=0; for(k=0,2*n,t=polcoeff((1+x-2*x^2)^n,k,x); S=S+abs(t)); print1(S","))

SageMath

def A084612(n,k): return sum(binomial(n,k-j)*binomial(k-j,j)*(-2)^j for j in range(k+1))
def A084613(n): return sum(abs(A084612(n,k)) for k in range(2*n+1))
[A084613(n) for n in range(51)] # G. C. Greubel, Mar 25 2023