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A093112 Carol numbers. 2
-1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, 4190207, 16769023, 67092479, 268402687, 1073676287, 4294836223, 17179607039, 68718952447, 274876858367, 1099509530623, 4398042316799, 17592177655807, 70368727400447, 281474943156223, 1125899839733759 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Carol Number

Index to sequences with linear recurrences with constant coefficients, signature (6,-7,-6,8).

FORMULA

a(n) = (2^n-1)^2-2.

a(n) = 6*a(n-1)-7*a(n-2)-6*a(n-3)+8*a(n-4). G.f.: x*(16*x^2-14*x+1) / ((x-1)*(2*x-1)*(4*x-1)). - Colin Barker, Jul 07 2014

MAPLE

[seq (((stirling2(n, 2))^2-2), n=2..23)]; - Zerinvary Lajos, Dec 20 2006

MATHEMATICA

lst={}; Do[p=(2^n-1)^2-2; AppendTo[lst, p], {n, 66}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)

PROG

(PARI) Vec(x*(16*x^2-14*x+1)/((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jul 07 2014

CROSSREFS

Cf. A000225.

Sequence in context: A201437 A202509 A009202 * A091516 A064385 A009260

Adjacent sequences:  A093109 A093110 A093111 * A093113 A093114 A093115

KEYWORD

sign,easy

AUTHOR

Eric W. Weisstein, Mar 20, 2004

EXTENSIONS

More terms from Colin Barker, Jul 07 2014

STATUS

approved

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Last modified August 29 22:27 EDT 2014. Contains 246212 sequences.