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A158608 a(n)=a(n-1)+16*a(n-2), starting a(0)=1, a(1)=4. 4
1, 4, 20, 84, 404, 1748, 8212, 36180, 167572, 746452, 3427604, 15370836, 70212500, 316145876, 1439545876, 6497879892, 29530613908, 133496692180, 605986514708, 2741933589588, 12437717824916, 56308655258324, 255312140456980 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Quadratic equation associated with group [3,3,5] which instead of t=phi uses t=2 in Phi(t)=(1+Sqrt[1+4*t^4])/(2*t).

REFERENCES

H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973,page 221.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,16).

FORMULA

a(n) = A168579(n)+3*A168579(n-1).

G.f.: (1+3x)/(1-x-16*x^2). [From Philippe Deléham, Mar 26 2009]

a(n)=(1/2)*{[(1/2)-(1/2)*sqrt(65)]^n +[(1/2)+(1/2)*sqrt(65)]^n} +(7/130)*sqrt(65)*{[(1/ 2)+(1/2)*sqrt(65)]^n -[(1/2)-(1/2)*sqrt(65)]^n}, [From Paolo P. Lava, Mar 30 2009]

MATHEMATICA

Clear[M, v, t, n];

M = {{0, t}, {t, 1/t}};

v[0] = {1, 1};

v[n_] := v[n] = M.v[n - 1];

t = 2;

a = Table[t^n*v[n][[1]], {n, 0, 30}]

CROSSREFS

Sequence in context: A080674 A246936 A110154 * A282084 A262768 A250003

Adjacent sequences:  A158605 A158606 A158607 * A158609 A158610 A158611

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Mar 22 2009

EXTENSIONS

Definition simplified following the Deleham proposition of Mar 2009 - The Assoc. Eds. of the OEIS, Aug 29 2010

STATUS

approved

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Last modified September 18 20:22 EDT 2019. Contains 327181 sequences. (Running on oeis4.)