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A164541
a(n) = 6*a(n-1) - a(n-2) for n > 1; a(0) = 1, a(1) = 15.
3
1, 15, 89, 519, 3025, 17631, 102761, 598935, 3490849, 20346159, 118586105, 691170471, 4028436721, 23479449855, 136848262409, 797610124599, 4648812485185, 27095264786511, 157922776233881, 920441392616775
OFFSET
0,2
COMMENTS
Binomial transform of A164540. Third binomial transform of A164675. Inverse binomial transform of A164542.
FORMULA
a(n) = 6*a(n-1) - a(n-2) for n > 1; a(0) = 1, a(1) = 15.
G.f: (1+9*x)/(1-6*x+x^2).
a(n) = ((1+3*sqrt(2))*(3+2*sqrt(2))^n + (1-3*sqrt(2))*(3-2*sqrt(2))^n)/2.
MATHEMATICA
LinearRecurrence[{6, -1}, {1, 15}, 20] (* Harvey P. Dale, Feb 04 2023 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(3+2*r)^n+(1-3*r)*(3-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009
STATUS
approved