login
A073702
a(n) = A073145(n)^2.
1
9, 1, 1, 25, 25, 1, 121, 225, 9, 529, 1681, 441, 1849, 11025, 6889, 4225, 64009, 73441, 2209, 326041, 632025, 31329, 1413721, 4669921, 1320201, 4844401, 30371121, 19882681, 10582009, 174847729, 208196041, 4190209, 882030601, 1770810561
OFFSET
0,1
FORMULA
a(n) = -a(n-2) + 6*a(n-3) + 3*a(n-4) + 2*a(n-5) - a(n-6) with a(0)=9, a(1)=1, a(2)=1, a(3)=25, a(4)=25, a(5)=1.
G.f.: (9+x+10*x^2-28*x^3-7*x^4-x^5)/(1+x^2-6*x^3-3*x^4-2*x^5+x^6).
a(n) = 2*A001644(n) + A073496(n).
MATHEMATICA
CoefficientList[Series[(9+x+10x^2-28x^3-7x^4-x^5)/(1+x^2-6x^3-3x^4-2x^5 +x^6), {x, 0, 40}], x]
LinearRecurrence[{0, -1, 6, 3, 2, -1}, {9, 1, 1, 25, 25, 1}, 40] (* Harvey P. Dale, Feb 14 2015 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((9+x+10*x^2-28*x^3-7*x^4-x^5)/(1+x^2-6*x^3 -3*x^4-2*x^5+x^6)) \\ G. C. Greubel, Apr 23 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (9+x+ 10*x^2-28*x^3-7*x^4-x^5)/(1+x^2-6*x^3-3*x^4-2*x^5+x^6) )); // G. C. Greubel, Apr 23 2019
(Sage) ((9+x+10*x^2-28*x^3-7*x^4-x^5)/(1+x^2-6*x^3-3*x^4-2*x^5+x^6) ).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Aug 04 2002
STATUS
approved