A073702 a(n) = A073145(n)^2.

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

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 04 2002

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,-1,6,3,2,-1).

Crossrefs

Cf. A001644, A073145, A073496.

Programs

Magma

R:=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

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 *)

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

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

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).