OFFSET
0,2
COMMENTS
The first g.f. gives a 0 between each two terms of the sequence - Colin Barker, Jul 12 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,-4,11,-8,0,8,-10,0,8,0,-10,8,0,-8,11,-4,-4,4,-1).
FORMULA
G.f.: (30/(1-x^2)^8-70/(1-x^4)^4+120/(1-x^8)^2-64/(1-x^16))/16.
G.f.: (9*x^12 -21*x^11 +26*x^10 +121*x^9 -149*x^8 +132*x^7 +20*x^6 +68*x^5 -61*x^4 +89*x^3 -6*x^2 +11*x +1) / ((x-1)^8 *(x+1)^4 *(x^2+1)^2 *(x^4+1)). - Colin Barker, Jul 12 2013
a(n) = 4*a(n-1)-4*a(n-2)-4*a(n-3)+11*a(n-4)-8*a(n-5)+8*a(n-7)-10*a(n-8)+8*a(n-10)-10*a(n-12)+8*a(n-13)-8*a(n-15)+11*a(n-16)-4*a(n-17)-4*a(n-18)+4*a(n-19)-a(n-20). - Wesley Ivan Hurt, May 24 2021
MATHEMATICA
CoefficientList[Series[(9 x^12 - 21 x^11 + 26 x^10 + 121 x^9 - 149 x^8 + 132 x^7 + 20 x^6 + 68 x^5 - 61 x^4 + 89 x^3 - 6 x^2 + 11 x + 1)/((x - 1)^8 (x + 1)^4 (x^2 + 1)^2 (x^4 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 19 2013 *)
LinearRecurrence[{4, -4, -4, 11, -8, 0, 8, -10, 0, 8, 0, -10, 8, 0, -8, 11, -4, -4, 4, -1}, {1, 15, 50, 225, 590, 1485, 3130, 6435, 11931, 21450, 36220, 59670, 94140, 145350, 217500, 319770, 458981, 648945, 900350, 1233375}, 40] (* Harvey P. Dale, Aug 14 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Jul 13 2000
EXTENSIONS
More terms from James A. Sellers, Aug 08 2000
More terms from Colin Barker, Jul 12 2013
STATUS
approved