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A163448
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a(n) = 20*a(n-1)-98*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
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2
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1, 12, 142, 1664, 19364, 224208, 2586488, 29757376, 341671696, 3917211072, 44860395232, 513321219584, 5870105658944, 67096633659648, 766662318616448, 8757776273683456, 100022618249257216, 1142190290164165632
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A163447. Tenth binomial transform of A163403.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
| a(n) = ((1+sqrt(2))*(10+sqrt(2))^n+(1-sqrt(2))*(10-sqrt(2))^n)/2.
G.f.: (1-8*x)/(1-20*x+98*x^2).
a(n)=(31*(10-Sqrt[2])^n-41*Sqrt[2]*(10-Sqrt[2])^n+49*(10+Sqrt[2])^n+ 49*Sqrt[2]*(10+Sqrt[2])^n)/(98*(10+Sqrt[2])) [From Harvey P. Dale, Nov 14 2011]
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MATHEMATICA
| LinearRecurrence[{20, -98}, {1, 12}, 30] (* or *) With[{ms=10-Sqrt[2], ps=10+ Sqrt[2]}, Table[Simplify[(31ms^n-41Sqrt[2](ms^n)+49ps^n+49Sqrt[2] ps^n)/ (98ps)], {n, 20}]] (* From Harvey P. Dale, Nov 14 2011 *)
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PROG
| (MAGMA) [ n le 2 select 11*n-10 else 20*Self(n-1)-98*Self(n-2): n in [1..18] ];
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CROSSREFS
| Cf. A163447, A163403.
Sequence in context: A056340 A056330 A158516 * A172210 A171317 A004191
Adjacent sequences: A163445 A163446 A163447 * A163449 A163450 A163451
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KEYWORD
| nonn
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 27 2009
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