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A163473
a(n) = 14*a(n-1) - 46*a(n-2) for n > 1; a(0) = 3, a(1) = 24.
3
3, 24, 198, 1668, 14244, 122688, 1062408, 9230064, 80350128, 700318848, 6108357984, 53302344768, 465248359488, 4061569173504, 35460543892608, 309615432515328, 2703431036154624, 23605724610459648, 206122316883322368
OFFSET
0,1
COMMENTS
Binomial transform of A163472. Inverse binomial transform of A163474.
FORMULA
a(n) = ((3+sqrt(3))*(7+sqrt(3))^n + (3-sqrt(3))*(7-sqrt(3))^n)/2.
G.f.: (3-18*x)/(1-14*x+46*x^2).
E.g.f.: exp(7*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017
MATHEMATICA
LinearRecurrence[{14, -46}, {3, 24}, 50] (* G. C. Greubel, Jul 26 2017 *)
PROG
(Magma) [ n le 2 select 21*n-18 else 14*Self(n-1)-46*Self(n-2): n in [1..19] ];
(PARI) x='x+O('x^50); Vec((3-18*x)/(1-14*x+46*x^2)) \\ G. C. Greubel, Jul 26 2017
CROSSREFS
Sequence in context: A037769 A037657 A074580 * A063979 A308354 A370375
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Aug 11 2009
STATUS
approved