A118434 Row sums of self-inverse triangle A118433.

1, 0, 2, 4, -4, 0, -8, -16, 16, 0, 32, 64, -64, 0, -128, -256, 256, 0, 512, 1024, -1024, 0, -2048, -4096, 4096, 0, 8192, 16384, -16384, 0, -32768, -65536, 65536, 0, 131072, 262144, -262144, 0, -524288, -1048576, 1048576, 0, 2097152, 4194304, -4194304

Offset: 0

Author

Paul D. Hanna, Apr 28 2006

Keywords

• sign
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,-4).

Crossrefs

Cf. A118433.

Programs

Maple

A118434 := proc(n) I*(1-I)^n-I*(1+I)^n+(-1-I)^n+(-1+I)^n ; expand(%/2) ;end proc:
# R. J. Mathar, Jan 18 2011

Mathematica

a[n_] := 2^(Floor[(n+1)/2]-3)*(-2*Mod[n, 8] + Mod[n+2 , 8] - Mod[n+3, 8] + 2*Mod[n+4, 8] - Mod[n+6, 8] + Mod[n+7, 8]); Table[a[n], {n, 0, 44}] (* Jean-François Alcover, May 23 2013 *)

PARI

{a(n)=polcoeff((1+2*x^2+4*x^3)/(1+4*x^4+x*O(x^n)),n)}

PARI

/* E.g.f.: */
{a(n)=local(x=X+X*O(X^n));n!*polcoeff(cos(x)*exp(-x)+sin(x)*exp(x),n,X)}

Formula

O.g.f.: A(x) = (1+2*x^2+4*x^3)/(1+4*x^4).

E.g.f.: A(x) = cos(x)*exp(-x) + sin(x)*exp(x).

2*a(n) = i*(1-i)^n-i*(1+i)^n + (-1-i)^n + (-1+i)^n with i=sqrt(-1). - R. J. Mathar, Jan 18 2011