OFFSET
0,2
COMMENTS
A diagonal of the square array A217770.
LINKS
Index entries for linear recurrences with constant coefficients, signature (8,-21,20,-5).
FORMULA
G.f.: (1-5*x+7*x^2-3*x^3)/(1-8*x+21*x^2-20*x^3+5*x^4).
a(n) = A217770(n+1,n).
a(n) = 8*a(n-1) -21*a(n-2) +20*a(n-3) -5*a(n-4) for n>3, a(0)=1, a(1)=3, a(2)=10, a(3)=34.
a(n) = ((3+r)*(5+r)^n-(3-r)*(5-r)^n+(1+r)*(3+r)^n-(1-r)*(3-r)^n)/(4*r*2^n), where r=sqrt(5). [Bruno Berselli, Mar 28 2013]
MATHEMATICA
LinearRecurrence[{8, -21, 20, -5}, {1, 3, 10, 34}, 26] (* Bruno Berselli, Mar 28 2013 *)
CoefficientList[Series[(1-x)^2(1-3x)/((1-3x+x^2)(1-5x+5x^2)), {x, 0, 30}], x] (* Harvey P. Dale, Sep 26 2023 *)
PROG
(Magma) m:=26; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)^2*(1-3*x)/((1-3*x+x^2)*(1-5*x+5*x^2)))); // Bruno Berselli, Mar 28 2013
(Maxima) makelist(expand(((3+sqrt(5))*(5+sqrt(5))^n-(3-sqrt(5))*(5-sqrt(5))^n+(1+sqrt(5))*(3+sqrt(5))^n-(1-sqrt(5))*(3-sqrt(5))^n)/(4*2^n*sqrt(5))), n, 0, 25); /* Bruno Berselli, Mar 28 2013 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Mar 24 2013
STATUS
approved