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A120723
Expansion of x*(1+3*x)*(1+6*x+16*x^2)/((1-x)*(1+2*x)*(1-3*x-2*x^2)).
1
1, 11, 63, 247, 887, 3207, 11383, 40679, 144663, 515719, 1835831, 6540327, 23289943, 82955975, 295436919, 1052244583, 3747563927, 13347268359, 47536758199, 169305160871, 602988299991, 2147576619847, 7648703663351
OFFSET
1,2
FORMULA
G.f.: x*(1+3*x)*(1+6*x+16*x^2)/((1-x)*(1+2*x)*(1-3*x-2*x^2)). - Colin Barker, Apr 04 2012
a(n) = 12*[n=0] - 23/3 + (-2)^n/6 - (9/2)*(A007482(n) - 5*A007482(n- 1)). - G. C. Greubel, Jul 20 2023
MATHEMATICA
CoefficientList[Series[(1+3x)*(1 +6x +16x^2)/((1-x)*(1+2x)*(1-3x-2x^2)), {x, 0, 50}], x] (* Bruno Berselli, Apr 04 2012 *)
LinearRecurrence[{2, 7, -4, -4}, {1, 11, 63, 247}, 40] (* G. C. Greubel, Jul 20 2023 *)
PROG
(Magma) I:=[1, 11, 63, 247]; [n le 4 select I[n] else 2*Self(n-1) + 7*Self(n-2) -4*Self(n-3) -4*Self(n-4): n in [1..40]]; // G. C. Greubel, Jul 20 2023
(SageMath)
A007482=BinaryRecurrenceSequence(3, 2, 1, 3)
def A120723(n): return 12*int(n==0) - (1/6)*(46 - (-2)^n + 27*(A007482(n) - 5*A007482(n-1)))
[A120723(n) for n in range(41)] # G. C. Greubel, Jul 20 2023
CROSSREFS
Cf. A007482.
Sequence in context: A162946 A301610 A298046 * A053367 A163706 A180763
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Aug 17 2006
EXTENSIONS
Edited by N. J. A. Sloane, Jun 15 2007
Meaningful name from Joerg Arndt, Dec 26 2022
STATUS
approved