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A158608
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a(n)=a(n-1)+16*a(n-2), starting a(0)=1, a(1)=4.
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4
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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; internal format)
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OFFSET
| 0,2
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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).
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REFERENCES
| H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973,page 221.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,16).
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FORMULA
| a(n) = A168579(n)+3*A168579(n-1).
G.f.: (1+3x)/(1-x-16*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 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 (paoloplava(AT)gmail.com), Mar 30 2009]
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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}]
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CROSSREFS
| Sequence in context: A084240 A080674 A110154 * A196953 A093357 A027156
Adjacent sequences: A158605 A158606 A158607 * A158609 A158610 A158611
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KEYWORD
| nonn,easy
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 22 2009
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EXTENSIONS
| Definition simplified following the Deleham proposition of Mar 2009 - The Assoc. Eds. of the OEIS, Aug 29 2010
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