A173559 a(n)= +2*a(n-2) +4*a(n-3), n>3.

1, -6, -13, -27, -50, -106, -208, -412, -840, -1656, -3328, -6672, -13280, -26656, -53248, -106432, -213120, -425856, -851968, -1704192, -3407360, -6816256, -13631488, -27261952, -54528000, -109049856, -218103808, -436211712, -872407040, -1744838656

Offset: 0

Author

Paul Curtz, Feb 21 2010

Keywords

• sign
• easy

Comments

Generated by scanning the diagonal of the table generated by A143025 in the top row followed by higher order differences in the other rows:

1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8, 1, 8, 2, 8,...

7, -6, 6, -7, 7, -6, 6, -7, 7, -6, 6, -7, 7,...

-13, 12, -13, 14, -13, 12, -13, 14, -13, 12,..

25, -25, 27, -27, 25, -25, 27, -27, 25, -25,..

-50, 52, -54, 52, -50, 52, -54, 52, -50, 52, ...

102, -106, 106, -102, 102, -106, 106, -102,...

Links

• Index entries for linear recurrences with constant coefficients, signature (0,2,4).

Programs

Mathematica

LinearRecurrence[{0,2,4},{1,-6,-13,-27},30] (* Harvey P. Dale, Jan 27 2019 *)

Formula

a(n) = ( -13*2^n-2*A009116(n))/4, n>0.

a(n+1)-2*a(n) = -A137429(n-2), n>1.

G.f.: (6*x+15*x^2+19*x^3-1)/( (2*x-1) *(2*x^2+2*x+1)).