|
|
A084615
|
|
a(n) = sum of absolute values of coefficients of (1+x-3x^2)^n.
|
|
18
|
|
|
1, 5, 23, 99, 401, 1525, 6345, 27331, 122083, 520805, 2117293, 8301441, 34517395, 147850771, 628707981, 2675100397, 10920387779, 43701876543, 180872758207, 769658883325, 3243501133481, 13617178197183, 56148348498199
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
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
|
|
MATHEMATICA
|
Table[Total[Abs[CoefficientList[Expand[(1+x-3x^2)^n], x]]], {n, 0, 30}] (* Harvey P. Dale, Mar 26 2013 *)
|
|
PROG
|
(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", "))
(Magma)
A084614:= func< n, k | (&+[Binomial(n, k-j)*Binomial(k-j, j)*(-3)^j: j in [0..k]]) >;
(SageMath)
@CachedFunction
def A084614(n, k): return sum(binomial(n, k-j)*binomial(k-j, j)*(-3)^j for j in range(k+1))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|