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A125820 a(n) = ((1 + 7*sqrt(2))^n + (1 - 7*sqrt(2))^n)/2. 2
1, 1, 99, 295, 10193, 49001, 1086723, 6926543, 119265217, 910405105, 13389536259, 115088367703, 1528961752529, 14221495172249, 176752280339811, 1732989592387775, 20610950377737217, 209321891217088609, 2417905969074687267, 25140035386206969607 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

T. D. Noe, Table of n, a(n) for n = 1..200

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

FORMULA

From Philippe Deléham, Dec 12 2006: (Start)

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

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

MATHEMATICA

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

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

PROG

(PARI) my(x='x+O('x^30)); Vec((1-x)/(1-2*x-97*x^2)) \\ G. C. Greubel, Aug 03 2019

(MAGMA) I:=[1, 1]; [n le 2 select I[n] else 2*Self(n-1) +97*Self(n-2): n in [1..30]]; // G. C. Greubel, Aug 03 2019

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

(GAP) a:=[1, 1];; for n in [3..30] do a[n]:=2*a[n-1]+97*a[n-2]; od; a; # G. C. Greubel, Aug 03 2019

CROSSREFS

Cf. A125819.

Sequence in context: A260279 A250779 A259995 * A008902 A008882 A156757

Adjacent sequences:  A125817 A125818 A125819 * A125821 A125822 A125823

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 10 2006

STATUS

approved

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Last modified October 21 11:25 EDT 2019. Contains 328295 sequences. (Running on oeis4.)