A103644 Expansion of g.f. (3x+1)/((1-3*x)*(1+5*x+9*x^2)).
1, 1, 4, 25, 1, 256, 169, 1225, 5476, 961, 64009, 25600, 358801, 1164241, 515524, 15642025, 3243601, 101284096, 239228089, 216825625, 3736387876, 287336401, 27697946329, 47210598400
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Creighton Dement, Online Floretion Multiplier. [broken link]
- Index entries for linear recurrences with constant coefficients, signature (-2,6,27).
Crossrefs
Cf. A103645.
Programs
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Maple
A103644 := proc(n) 6*3^n+5*(-1)^n*A190970(n+1)+18*(-1)^(n+1)*A190970(n) ; %/11 ; end proc: seq(A103644(n),n=0..20) ; # R. J. Mathar, Mar 23 2023
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Mathematica
CoefficientList[Series[(3x+1)/(1+2x-6x^2-27x^3),{x,0,30}],x] (* or *) LinearRecurrence[{-2,6,27},{1,1,4},30] (* Harvey P. Dale, Dec 13 2017 *)
Formula
a(n+3) = -2a(n+2) + 6a(n+1) + 27a(n), a(0) = 1, a(1) = 1, a(2) = 4.
a(n) = (1/11)*(2*3^n-(-5/2-(I*sqrt(11))/2)^n-(-5/2+(I*sqrt(11))/2)^n). [Creighton Dement, May 24 2009]
11*a(n) = 6*3^n + 5*b(n) + 18*b(n-1) where b(n) = (-1)^n*A190970(n+1). - R. J. Mathar, Mar 23 2023
Extensions
Corrected by T. D. Noe, Nov 07 2006
Comments