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A100297
Expansion of g.f.: x*(1-11*x+x^2)/(1-17*x+14*x^2-x^3).
3
1, 6, 89, 1430, 23070, 372259, 6006853, 96927945, 1564051382, 25237889117, 407244323586, 6571387104706, 106037398138915, 1711043593219257, 27609788897887265, 445517838357152822, 7188977251094395521, 116002973320502471614, 1871850382771577632966
OFFSET
1,2
FORMULA
a(n) = 17*a(n-1) - 14*a(n-2) + a(n-3).
G.f.: x*(1-11*x+x^2)/(1-17*x+14*x^2-x^3). - Colin Barker, Dec 13 2012
EXAMPLE
a(6) = 372259 = 17*23070 - 14*1430 + 89 = 17*a(5) - 14*a(4) + a(3).
MATHEMATICA
LinearRecurrence[{17, -14, 1}, {1, 6, 89}, 20] (* Harvey P. Dale, Mar 14 2022 *)
PROG
(Magma) I:=[1, 6, 89]; [n le 3 select I[n] else 17*Self(n-1) -14*Self(n-2) +Self(n-3): n in [1..31]]; // G. C. Greubel, Feb 05 2023
(SageMath)
@CachedFunction
def a(n): # a = A100297
if (n<3): return (1, 1, 6)[n]
else: return 17*a(n-1) - 14*a(n-2) + a(n-3)
[a(n) for n in range(1, 31)] # G. C. Greubel, Feb 05 2023
CROSSREFS
Sequence in context: A054952 A101148 A355187 * A177568 A177573 A166782
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Nov 11 2004
EXTENSIONS
More terms from Colin Barker, Dec 13 2012
New name using g.f. from Joerg Arndt, Aug 31 2024
STATUS
approved