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A129589 a(n) = 2*A000129(n) + A000129(n-1) - n. 1
1, 3, 9, 25, 65, 163, 401, 977, 2369, 5731, 13849, 33449, 80769, 195011, 470817, 1136673, 2744193, 6625091, 15994409, 38613945, 93222337, 225058659, 543339697, 1311738097, 3166815937, 7645370019, 18457556025, 44560482121, 107578520321, 259717522819 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n)/a(n-1) tends to 1 + sqrt(2).
LINKS
FORMULA
a(n) = 2*A000129(n) + A000129(n-1) - n; where A000129 = the Pell sequence. a(n) = A000129(n+1) - n.
From Colin Barker, Sep 02 2019: (Start)
G.f.: x*(1 - x + x^2 + x^3) / ((1 - x)^2*(1 - 2*x - x^2)).
a(n) = (-(1 - sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / (2*sqrt(2)) - n.
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-4) for n>4.
(End)
EXAMPLE
a(5) = 65 = 2*A000129(5) + A000129(4) - 5 = 2*29 + 12 - 5.
a(5) = 65 = A000129(6) - 5 = 70 - 5.
PROG
(PARI) Vec(x*(1 - x + x^2 + x^3) / ((1 - x)^2*(1 - 2*x - x^2)) + O(x^35)) \\ Colin Barker, Sep 02 2019
CROSSREFS
Cf. A000129.
Sequence in context: A195417 A295142 A002064 * A335472 A096322 A058396
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Sep 19 2007
STATUS
approved

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Last modified April 18 15:48 EDT 2024. Contains 371780 sequences. (Running on oeis4.)