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

0,5

Comments

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

Links

Table of n, a(n) for n=0..33.

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

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

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 *)

Crossrefs

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

Sequence in context: A000742 A362419 A301134 * A008234 A008114 A301139

Adjacent sequences: A132149 A132150 A132151 * A132153 A132154 A132155

Keyword

nonn,easy

Author

Paul Curtz, Nov 01 2007

Extensions

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

Status

approved