%I #17 Jun 13 2015 00:53:00

%S 1,2,-5,-1,-11,-13,-35,-61,-131,-253,-515,-1021,-2051,-4093,-8195,

%T -16381,-32771,-65533,-131075,-262141,-524291,-1048573,-2097155,

%U -4194301,-8388611,-16777213,-33554435,-67108861,-134217731,-268435453,-536870915,-1073741821,-2147483651

%N a(0)=1. a(n)= -2^(n-1)-3*(-1)^n, n>1.

%C The main diagonal of the array of A153130 and its successive differences.

%C A154589 is the second upper diagonal of the array.

%H Vincenzo Librandi, <a href="/A156067/b156067.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).

%F a(n)= +a(n-1) +2*a(n-2), n>2.

%F G.f.: x*(-2+7*x) / ( (1+x)*(2*x-1) ).

%F a(n) == A153130(n) (mod 9).

%F a(n+1)-2*a(n) = (-1)^n*9, n>0.

%F a(n) = A154589(n)-3*(-1)^n.

%F a(n)+a(n+3) = -A005010(n-1) = -9*A131577(n).

%F a(2*n)+a(2*n+1) = -3*2^(2n-1) = -A002023(n-2).

%t Join[{1},LinearRecurrence[{1,2},{2,-5},40]] (* _Harvey P. Dale_, Dec 11 2011 *)

%K easy,sign

%O 0,2

%A _Paul Curtz_, Feb 03 2009