A086351 - OEIS

A086351

T(n,3) of A086350.

1, 4, 17, 74, 325, 1432, 6317, 27878, 123049, 543148, 2397545, 10583234, 46716589, 206216896, 910285253, 4018193246, 17737162705, 78295623508, 345613602113, 1525612248122, 6734378273941, 29726983906792, 131221255523165

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OFFSET

0,2

COMMENTS

Binomial transform of A007052. Second binomial transform of Pell numbers A000129 (without leading zero).

LINKS

Table of n, a(n) for n=0..22.

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

FORMULA

G.f.: (1-2x)/(1-6x+7x^2);

a(n)=((1+sqrt(2))(3+sqrt(2))^n-(1-sqrt(2))(3-sqrt(2))^n)/(sqrt(8)).

a(n) = A081179(n+1)-2*A081179(n). - R. J. Mathar, Dec 05 2022

PROG

(PARI) a(n)=my(sqrt2=quadgen(8)); simplify(((1+sqrt2)*(3+sqrt2)^n-(1-sqrt2)*(3-sqrt2)^n)/sqrt2^3) \\ Charles R Greathouse IV, Oct 24 2014

CROSSREFS

Sequence in context: A363541 A184700 A125586 * A049027 A026751 A227504

Adjacent sequences: A086348 A086349 A086350 * A086352 A086353 A086354

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 18 2003

STATUS

approved