A156067 a(0)=1. a(n)= -2^(n-1)-3*(-1)^n, n>1.

1, 2, -5, -1, -11, -13, -35, -61, -131, -253, -515, -1021, -2051, -4093, -8195, -16381, -32771, -65533, -131075, -262141, -524291, -1048573, -2097155, -4194301, -8388611, -16777213, -33554435, -67108861, -134217731, -268435453, -536870915, -1073741821, -2147483651

Offset: 0

Author

Paul Curtz, Feb 03 2009

Keywords

• easy
• sign

Comments

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

A154589 is the second upper diagonal of the array.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Programs

Mathematica

Join[{1},LinearRecurrence[{1,2},{2,-5},40]] (* Harvey P. Dale, Dec 11 2011 *)

Formula

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

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

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

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

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

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

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