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

0,2

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).

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).

Mathematica

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

Crossrefs

Sequence in context: A089618 A207629 A207614 * A352577 A263487 A101920

Adjacent sequences: A156064 A156065 A156066 * A156068 A156069 A156070

Keyword

easy,sign

Author

Paul Curtz, Feb 03 2009

Status

approved