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A100295
Expansion of g.f. x*(1-x)/(1-4*x-2*x^2+x^3).
2
1, 3, 14, 61, 269, 1184, 5213, 22951, 101046, 444873, 1958633, 8623232, 37965321, 167149115, 735903870, 3239948389, 14264452181, 62801801632, 276496162501, 1217323801087, 5359485727718, 23596094350545, 103886025056529, 457376803199488, 2013683168560465
OFFSET
1,2
FORMULA
a(n) = 4*a(n-1) + 2*a(n-2) - a(n-3).
G.f.: x*(1-x)/(1-4*x-2*x^2+x^3). - Colin Barker, May 25 2013
MAPLE
a:= n-> (<<3|2|1>, <2|1|0>, <1|0|0>>^n)[1, 3]:
seq(a(n), n=1..30); # Alois P. Heinz, May 25 2013
MATHEMATICA
LinearRecurrence[{4, 2, -1}, {1, 3, 14}, 40] (* G. C. Greubel, Feb 05 2023 *)
PROG
(Magma) I:=[1, 3, 14]; [n le 3 select I[n] else 4*Self(n-1) +2*Self(n-2) -Self(n-3): n in [1..40]]; // G. C. Greubel, Feb 05 2023
(SageMath)
@CachedFunction
def a(n): # a = A100296
if (n<3): return (0, 1, 3)[n]
else: return 4*a(n-1) + 2*a(n-2) - a(n-3)
[a(n) for n in range(1, 41)] # G. C. Greubel, Feb 05 2023
CROSSREFS
Sequence in context: A281349 A307268 A237608 * A291025 A320499 A091701
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Nov 11 2004
EXTENSIONS
More terms from Colin Barker, May 25 2013
New name using g.f. from Joerg Arndt, Aug 31 2024
STATUS
approved