A084615 - OEIS

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

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OFFSET

0,2

LINKS

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

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]]) >;

[(&+[Abs(A084614(n, k)): k in [0..2*n]]): n in [0..50]]; // G. C. Greubel, Mar 25 2023

(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

CROSSREFS

Cf. A002426, A084600 - A084614.

Sequence in context: A368835 A119012 A215038 * A181331 A268400 A364754

Adjacent sequences: A084612 A084613 A084614 * A084616 A084617 A084618

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 01 2003

STATUS

approved