A100297 Expansion of g.f.: x*(1-11*x+x^2)/(1-17*x+14*x^2-x^3).

1, 6, 89, 1430, 23070, 372259, 6006853, 96927945, 1564051382, 25237889117, 407244323586, 6571387104706, 106037398138915, 1711043593219257, 27609788897887265, 445517838357152822, 7188977251094395521, 116002973320502471614, 1871850382771577632966

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..825

Index entries for linear recurrences with constant coefficients, signature (17,-14,1).

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

Adjacent sequences: A100294 A100295 A100296 * A100298 A100299 A100300

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