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

0,2

Links

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

Mathematica

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

Prog

(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", "))
(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
(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

Crossrefs

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

Sequence in context: A292718 A212688 A261451 * A099063 A057223 A007466

Adjacent sequences: A084610 A084611 A084612 * A084614 A084615 A084616

Keyword

nonn

Author

Paul D. Hanna, Jun 01 2003

Status

approved