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A094703
a(n) = 8*a(n-1) + 21*a(n-2), with a(1)=1, a(2)=11.
3
1, 11, 109, 1103, 11113, 112067, 1129909, 11392679, 114869521, 1158202427, 11677879357, 117745285823, 1187197753081, 11970233026931, 120693017030149, 1216919029806743, 12269905596087073, 123714544394638187, 1247384372674934029, 12577080413686874159
OFFSET
1,2
FORMULA
Limit_{n -> oo} a(n+1)/a(n) converges to 4 + sqrt(37).
G.f.: x*(1+3*x)/(1-8*x-21*x^2). - Colin Barker, May 22 2015
a(n) = A093103(n+1) + 3*A093103(n). - G. C. Greubel, Feb 09 2023
MATHEMATICA
LinearRecurrence[{8, 21}, {1, 11}, 41] (* G. C. Greubel, Feb 09 2023 *)
PROG
(PARI) Vec(x*(1+3*x)/(1-8*x-21*x^2) + O(x^40)) \\ Colin Barker, May 22 2015
(Magma) [n le 2 select 10*n-9 else 8*Self(n-1) +21*Self(n-2): n in [1..41]]; // G. C. Greubel, Feb 09 2023
(SageMath)
@CachedFunction
def a(n): # a = A094703
if (n<3): return 10*n-9
else: return 8*a(n-1) + 21*a(n-2)
[a(n) for n in range(1, 41)] # G. C. Greubel, Feb 09 2023
CROSSREFS
Sequence in context: A054320 A287836 A124290 * A324355 A331537 A169631
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, May 21 2004
EXTENSIONS
More terms from Robert G. Wilson v, May 24 2004
Edited by Don Reble, Nov 04 2005
STATUS
approved