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A155196 a(n)=7*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=6, a(2)=42 . 1
1, 6, 42, 300, 2142, 15294, 109200, 779694, 5567058, 39749100, 283810758, 2026424406, 14468781600, 103307895606, 737624050842, 5266676251500, 37604357811342, 268497180930894, 1917084624327600, 13688089551224094 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (7, 1).

FORMULA

G.f.: (1-x-x^2)/(1-7*x-x^2).

a(n)=3*{[(7/2)+(1/2)*sqrt(53)]^(n-1)+[(7/2)-(1/2)*sqrt(53)]^(n-1)}+(21/53)*sqrt(53)*{[(7/2)+(1/2)*sqrt(53)]^(n-1)-[(7/2)-(1/2)*sqrt(53)]^(n-1)}+[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Jan 26 2009]

a(n) = Sum_{k, 0<=k<=n} A155161(n,k)*6^k. - Philippe Deléham, Feb 08 2012

MATHEMATICA

Join[{1}, LinearRecurrence[{7, 1}, {6, 42}, 20]] (* Harvey P. Dale, Sep 04 2014 *)

CROSSREFS

Sequence in context: A156361 A216517 A055272 * A147838 A127628 A111602

Adjacent sequences:  A155193 A155194 A155195 * A155197 A155198 A155199

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Jan 21 2009

STATUS

approved

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Last modified May 15 15:46 EDT 2021. Contains 343920 sequences. (Running on oeis4.)