A084615 a(n) = sum of absolute values of coefficients of (1+x-3x^2)^n.

1, 5, 23, 99, 401, 1525, 6345, 27331, 122083, 520805, 2117293, 8301441, 34517395, 147850771, 628707981, 2675100397, 10920387779, 43701876543, 180872758207, 769658883325, 3243501133481, 13617178197183, 56148348498199

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 - A084614.

Programs

Magma

A084614:= func< n,k | (&+[Binomial(n, k-j)*Binomial(k-j, j)*(-3)^j: j in [0..k]]) >;
[(&+[Abs(A084614(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-3x^2)^n],x]]],{n,0,30}] (* Harvey P. Dale, Mar 26 2013 *)

PARI

for(n=0,40,S=0; for(k=0,2*n,t=polcoeff((1+x-3*x^2)^n,k,x); S=S+abs(t)); print1(S","))

SageMath

@CachedFunction
def A084614(n,k): return sum(binomial(n,k-j)*binomial(k-j,j)*(-3)^j for j in range(k+1))
def A084615(n): return sum(abs(A084614(n,k)) for k in range(2*n+1))
[A084615(n) for n in range(50)] # G. C. Greubel, Mar 25 2023

Formula

a(n) = Sum_{k=0..2*n} abs( Sum_{j=0..k} binomial(n,k-j)*binomial(k-j,j)*(-3)^j ). - G. C. Greubel, Mar 25 2023