A019484 Expansion of (8 + 7 x - 7 x^2 - 7 x^3)/(1 - 6 x - 7 x^2 + 5 x^3 + 6 x^4).

8, 55, 379, 2612, 18002, 124071, 855106, 5893451, 40618081, 279942687, 1929384798, 13297456486, 91647010581, 631637678776, 4353291555505, 30003193292641, 206784130187015, 1425170850320396, 9822378297435246, 67696525926163327, 466569244606302614

Offset

0,1

Comments

Agrees with A010918 for terms 0 through 11055 but then differs from it.

a(11056) = 4971494197...7586894094 (9270 digits) = A010918(11056) - 1. - Jianing Song, Oct 15 2021

References

R. K. Guy, personal communication.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,7,-5,-6).

Index entries for sequences which agree for a long time but are different

Formula

G.f.: (8 + 7 x - 7 x^2 - 7 x^3)/(1 - 6 x - 7 x^2 + 5 x^3 + 6 x^4).

Maple

- (8 + 7*x - 7*x^2 - 7*x^3) /(7*x^2 - 1 + 6*x - 6*x^4 - 5*x^3);

Mathematica

CoefficientList[ Series[(8 + 7 x - 7 x^2 - 7 x^3)/(1 - 6 x - 7 x^2 + 5 x^3 + 6 x^4), {x, 0, 18}], x] (* Robert G. Wilson v, May 16 2008 *)
LinearRecurrence[{6, 7, -5, -6}, {8, 55, 379, 2612}, 20] (* Harvey P. Dale, Apr 20 2017 *)

Prog

(Magma) I:=[8, 55, 379, 2612]; [n le 4 select I[n] else 6*Self(n-1)+7*Self(n-2)-5*Self(n-3)-6*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Apr 21 2017

Crossrefs

Cf. A010918.

Sequence in context: A010924 A308687 A010918 * A108984 A264342 A230963

Adjacent sequences: A019481 A019482 A019483 * A019485 A019486 A019487

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

The old definition was a(n) = 3*a(n-1) + a(n-2) - 2*a(n-3), but as R. J. Mathar pointed out, this did not match the entries. I have therefore replaced the definition with a g.f. found by Superseeker. - N. J. A. Sloane, May 16 2008

Status

approved