A077397 Expansion of (1+31*x-2*x^2-2*x^3)/(1-16*x^2+x^4).

1, 31, 14, 494, 223, 7873, 3554, 125474, 56641, 1999711, 902702, 31869902, 14386591, 507918721, 229282754, 8094829634, 3654137473, 129009355423, 58236916814, 2056054857134, 928136531551, 32767868358721, 14791947588002, 522229838882402, 235743024876481

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,16,0,-1).

Crossrefs

Used for calculating the values in A077398

Programs

Magma

Q:=Rationals(); R:=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

Mathematica

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

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

Formula

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

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

a(n) = 16*a(n-2) - a(n-4) for n>3. - Colin Barker, Jul 27 2020

Extensions

More terms from Harvey P. Dale, Mar 25 2011