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A105036 a(0) = 0, a(1) = 4, a(2) = 8, a(3) = 116, for n>3 a(n) = 26*a(n-2) - a(n-4) + 12. 2
0, 4, 8, 116, 220, 3024, 5724, 78520, 148616, 2038508, 3858304, 52922700, 100167300, 1373951704, 2600491508, 35669821616, 67512611920, 926041410324, 1752727418424, 24041406846820, 45503400267116, 624150536607008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

It appears this sequence gives all the nonnegative m such that 42*n^2 + 42*n + 1 is a square.

LINKS

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (1, 26, -26, -1, 1).

FORMULA

a(n)=-1/2-1/6*(-1)^n*(13 + 2*sqrt(42))^(1/2*n)*(13 + 2*sqrt(42))^(1/4*(-1)^n)*sqrt(42) *(13 + 2*sqrt(42))^(-1/4)-(-1)^n*(13 + 2*sqrt(42))^(1/2*n)*(13 + 2*sqrt(42))^(1/4*( -1)^n)*(13 + 2*sqrt(42))^(-1/4) + 5/28*(13 + 2*sqrt(42))^(1/2*n)*(13 + 2*sqrt(42))^(1/4 *(-1)^n)*sqrt(42)*(13 + 2*sqrt(42))^(-1/4) + 5/4*(13 + 2*sqrt(42))^(1/2*n)*(13 + 2 *sqrt(42))^(1/4*(-1)^n)*(13 + 2*sqrt(42))^(-1/4) + 1/6*(-1)^n*(13-2*sqrt(42))^(-1/4) *(13-2*sqrt(42))^(1/2*n)*(13-2*sqrt(42))^(1/4*(-1)^n)*sqrt(42) + 5/4*(13-2 *sqrt(42))^(-1/4)*(13-2*sqrt(42))^(1/2*n)*(13-2*sqrt(42))^(1/4*(-1)^n)-(-1)^n *(13-2*sqrt(42))^(-1/4)*(13-2*sqrt(42))^(1/2*n)*(13-2*sqrt(42))^(1/4*(-1)^n)-5/28*(13-2*sqrt(42))^(-1/4)*(13-2*sqrt(42))^(1/2*n)*(13-2*sqrt(42))^(1/4*(-1)^n) *sqrt(42), with n>=0 [From Paolo P. Lava, Aug 28 2009]

G.f.: 4*x*(1+x+x^2)/((1-x)*(x^4-26*x^2+1)). a(n) = a(n-1)+26*a(n-2)-26*a(n-3)-a(n-4)+a(n-5). [From R. J. Mathar, Sep 13 2009]

a(2n) = (1/2)*[A097309(n+2)-9*A097309(n+1)-1], a(2n+1) = (1/2)*[9*A097309(n+2)-A097309(n+1)-1]. -- Ralf Stephan, Nov 15 2010.

MATHEMATICA

LinearRecurrence[{1, 26, -26, -1, 1}, {0, 4, 8, 116, 220}, 30] (* Harvey P. Dale, Mar 25 2013 *)

CROSSREFS

Sequence in context: A273060 A215844 A111100 * A012940 A182967 A013049

Adjacent sequences:  A105033 A105034 A105035 * A105037 A105038 A105039

KEYWORD

nonn

AUTHOR

Gerald McGarvey, Apr 03 2005

STATUS

approved

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Last modified July 5 07:06 EDT 2020. Contains 335460 sequences. (Running on oeis4.)