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A125819 a(n) = ((1 + 7*sqrt(2))^n - (1 - 7*sqrt(2))^n)/(14*sqrt(2)). 2
0, 1, 2, 101, 396, 10589, 59590, 1146313, 8072856, 127338073, 1037743178, 14427279437, 129515647140, 1658477399669, 15879972571918, 192632252911729, 1925621845299504, 22536572223036721, 231858463440125330, 2649764432514812597, 27789799818721782204 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

T. D. Noe, Table of n, a(n) for n = 0..199 (offset adapted by Georg Fischer, Jan 31 2019)

Index entries for linear recurrences with constant coefficients, signature (2, 97).

FORMULA

From Philippe Deléham, Dec 12 2006: (Start)

a(0)=0, a(1)=1, a(n) = 2*a(n-1) + 97*a(n-2) for n>=2.

G.f.: x/(1 - 2*x - 97*x^2). (End)

a(n) = -(-97)^n * a(-n) for all n in Z. - Michael Somos, Aug 17 2018

EXAMPLE

G.f. = x + 2*x^2 + 101*x^3 + 396*x^4 + 10589*x^5 + 59590*x^6 + ... - Michael Somos, Aug 17 2018

MATHEMATICA

Expand[Table[((1+7Sqrt[2])^n -(1-7Sqrt[2])^n)/(14Sqrt[2]), {n, 0, 30}]] (* Artur Jasinski *)

LinearRecurrence[{2, 97}, {0, 1}, 30] (* T. D. Noe, Mar 28 2012 *)

a[ n_] := Sqrt[-97]^(n - 1) ChebyshevU[n - 1, 1 / Sqrt[-97]]; (* Michael Somos, Aug 17 2018 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(x/(1 - 2*x - 97*x^2))) \\ G. C. Greubel, Aug 17 2018

(PARI) {a(n) = my(t = quadgen(-97*4)); simplify( polchebyshev(n-1, 2, 1/t) * t^(n-1))}; /* Michael Somos, Aug 17 2018 *)

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 2*Self(n-1) + 97*Self(n-2): n in [1..30]]; // G. C. Greubel, Aug 17 2018

(Sage) (x/(1-2*x-97*x^2)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Aug 03 2019

(GAP) a:=[0, 1];; for n in [3..30] do a[n]:=2*a[n-1]+97*a[n-2]; od; a; # G. C. Greubel, Aug 0232019

CROSSREFS

Cf. A125820.

Sequence in context: A064152 A162353 A088272 * A179998 A072383 A037053

Adjacent sequences:  A125816 A125817 A125818 * A125820 A125821 A125822

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 10 2006, corrected Jan 12 2007

EXTENSIONS

Offset corrected to 0. - Michael Somos, Aug 17 2018

STATUS

approved

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Last modified October 14 04:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)