%I #20 Jan 11 2025 05:20:34

%S 1,31,14,494,223,7873,3554,125474,56641,1999711,902702,31869902,

%T 14386591,507918721,229282754,8094829634,3654137473,129009355423,

%U 58236916814,2056054857134,928136531551,32767868358721,14791947588002,522229838882402,235743024876481

%N Expansion of (1+31*x-2*x^2-2*x^3)/(1-16*x^2+x^4).

%H G. C. Greubel, <a href="/A077397/b077397.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,16,0,-1).

%F a(2*n+4) = 16*a(2*n+2) - a(2*n), with a(0)=1, a(2)=14;

%F a(2*n+5) = 16*a(2*n+3) - a(2n+1), with a(1)=31, a(3)=494.

%F a(n) = 16*a(n-2) - a(n-4) for n>3. - _Colin Barker_, Jul 27 2020

%t CoefficientList[Series[(1+31x-2x^2-2x^3)/(1-16x^2+x^4), {x,0,40}],x] (* _Harvey P. Dale_, Mar 25 2011 *)

%o (PARI) my(x='x+O('x^30)); Vec((1+31*x-2*x^2-2*x^3)/(1-16*x^2+x^4)) \\ _G. C. Greubel_, Jan 18 2018

%o (Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q,30); Coefficients(R!((1+31*x-2*x^2-2*x^3)/(1-16*x^2+x^4))); // _G. C. Greubel_, Jan 18 2018

%Y Used for calculating the values in A077398

%K easy,nonn

%O 0,2

%A Bruce Corrigan (scentman(AT)myfamily.com), Nov 05 2002

%E More terms from _Harvey P. Dale_, Mar 25 2011