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A084156 Binomial transform of sinh(x)*cosh(sqrt(3)*x). 2
0, 1, 2, 13, 44, 181, 662, 2521, 9368, 35113, 130922, 489061, 1824836, 6811741, 25420670, 94875313, 354076208, 1321442641, 4931681234, 18405321661, 68689566044, 256353060613, 956722558310, 3570537526921, 13325427195080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (4,2,-12,3).

FORMULA

a(n) = 4*a(n-1)+2*a(n-2)-12*a(n-3)+3*a(n-4), a(0)=0, a(1)=1.

a(n) = ((2+sqrt(3))^n+(2-sqrt(3))^n-(sqrt(3))^n-(-sqrt(3))^n)/4.

G.f.: x*(1-2*x+3*x^2)/((1-3*x^2)(1-4*x+x^2)).

E.g.f. : exp(x)*sinh(x)*cosh(sqrt(3)*x).

MATHEMATICA

LinearRecurrence[{4, 2, -12, 3}, {0, 1, 2, 13}, 30] (* Harvey P. Dale, Feb 01 2014 *)

PROG

(MAGMA) I:=[0, 1, 2, 13]; [n le 4 select I[n] else 4*Self(n-1)+2*Self(n-2)-12*Self(n-3)+3*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 13 2014

CROSSREFS

Cf. A084157, A084154.

Sequence in context: A296807 A308731 A025194 * A002534 A212501 A117717

Adjacent sequences:  A084153 A084154 A084155 * A084157 A084158 A084159

KEYWORD

nonn,easy

AUTHOR

Paul Barry, May 16 2003

STATUS

approved

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)