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%I #13 Apr 19 2023 09:44:13
%S 0,0,0,1,4,10,20,34,56,100,200,356,624,1160,2320,4104,7136,13200,
%T 26400,46736,81344,150560,301120,533024,927616,1716800,3433600,
%U 6078016,10577664,19576960,39153920,69308544,120618496,223238400
%N 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.
%C a(n+1)-2a(n)= 0, 0, 1, 2, 2, 0, -6, -12, -12, 0, -44, -88, -88, 0
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 10, 0, 0, 0, 16).
%F Sequence is identical to its fourth differences in absolute value.
%F a(n)=10*a(n-4)+16*a(n-8), n>8. - _R. J. Mathar_, Feb 07 2009
%F 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
%t 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 *)
%Y Cf. A000749 (0, 0, 0, 1, 4, 10, 20, 36) for which a(n)=4a(n-1)-6a(n-2)+4a(n-3).
%K nonn,easy
%O 0,5
%A _Paul Curtz_, Nov 01 2007
%E Definition corrected and the sequence extended by _R. J. Mathar_, Feb 07 2009
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