A084615 - OEIS

%I #13 Mar 25 2023 08:20:24

%S 1,5,23,99,401,1525,6345,27331,122083,520805,2117293,8301441,34517395,

%T 147850771,628707981,2675100397,10920387779,43701876543,180872758207,

%U 769658883325,3243501133481,13617178197183,56148348498199

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

%H G. C. Greubel, <a href="/A084615/b084615.txt">Table of n, a(n) for n = 0..1000</a>

%F 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

%t Table[Total[Abs[CoefficientList[Expand[(1+x-3x^2)^n],x]]],{n,0,30}] (* _Harvey P. Dale_, Mar 26 2013 *)

%o (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","))

%o (Magma)

%o A084614:= func< n,k | (&+[Binomial(n, k-j)*Binomial(k-j, j)*(-3)^j: j in [0..k]]) >;

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

%o (SageMath)

%o @CachedFunction

%o def A084614(n,k): return sum(binomial(n,k-j)*binomial(k-j,j)*(-3)^j for j in range(k+1))

%o def A084615(n): return sum(abs(A084614(n,k)) for k in range(2*n+1))

%o [A084615(n) for n in range(50)] # _G. C. Greubel_, Mar 25 2023

%Y Cf. A002426, A084600 - A084614.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 01 2003