A132152 a(4n+k) = 4a(4n+k-1)-6a(4n+k-2)+4a(4n+k-3), for k = 0,1,2; 2*a(4n+3) = 7a(4n+2)-8(4n+1)+2a(4n), with a(0) = a(1) = a(2) = 0, a(3) = 1.

0, 0, 0, 1, 4, 10, 20, 34, 56, 100, 200, 356, 624, 1160, 2320, 4104, 7136, 13200, 26400, 46736, 81344, 150560, 301120, 533024, 927616, 1716800, 3433600, 6078016, 10577664, 19576960, 39153920, 69308544, 120618496, 223238400

Offset: 0

Author

Paul Curtz, Nov 01 2007

Keywords

• nonn
• easy

Comments

a(n+1)-2a(n)= 0, 0, 1, 2, 2, 0, -6, -12, -12, 0, -44, -88, -88, 0

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 10, 0, 0, 0, 16).

Crossrefs

Cf. A000749 (0, 0, 0, 1, 4, 10, 20, 36) for which a(n)=4a(n-1)-6a(n-2)+4a(n-3).

Programs

Mathematica

Join[{0},LinearRecurrence[{0,0,0,10,0,0,0,16},{0,0,1,4,10,20,34,56},40]] (* Harvey P. Dale, Nov 03 2013 *)

Formula

Sequence is identical to its fourth differences in absolute value.

a(n)=10*a(n-4)+16*a(n-8), n>8. - R. J. Mathar, Feb 07 2009

G.f.: -x^3*(2*x+1)*(4*x^2+1)*(2*x^2+2*x+1)/(-1+10*x^4+16*x^8) . - R. J. Mathar, Apr 19 2023

Extensions

Definition corrected and the sequence extended by R. J. Mathar, Feb 07 2009