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A048746
Partial sums of A048655.
2
1, 6, 17, 44, 109, 266, 645, 1560, 3769, 9102, 21977, 53060, 128101, 309266, 746637, 1802544, 4351729, 10506006, 25363745, 61233500, 147830749, 356895002, 861620757, 2080136520, 5021893801, 12123924126, 29269742057, 70663408244, 170596558549, 411856525346, 994309609245
OFFSET
0,2
FORMULA
a(n) = 2*a(n-1) + a(n-2) + 4; a(0)=1, a(1)=6.
a(n) = ((6 + 5*sqrt(2))*(1 + sqrt(2))^n + (6 - 5*sqrt(2))*(1 - sqrt(2))^n)/4 - 2. [Corrected by Stefano Spezia, May 26 2024]
From Colin Barker, Sep 19 2012: (Start)
a(n) = 3*a(n-1) - a(n-2) - a(n-3).
G.f.: (1+3*x)/((1-x)*(1-2*x-x^2)). (End)
a(n) = 2*Pell(n) + 3*Pell(n+1) - 2, where Pell = A000129. - Vladimir Reshetnikov, Sep 27 2016
E.g.f.: exp(x)*(6*cosh(sqrt(2)*x) + 5*sqrt(2)*sinh(sqrt(2)*x) - 4)/2. - Stefano Spezia, May 26 2024
MATHEMATICA
Accumulate[LinearRecurrence[{2, 1}, {1, 5}, 30]] (* Harvey P. Dale, May 23 2012 *)
LinearRecurrence[{3, -1, -1}, {1, 6, 17}, 26] (* Ray Chandler, Aug 03 2015 *)
Table[2 Fibonacci[n, 2] + 3 Fibonacci[n + 1, 2] - 2, {n, 0, 10}] (* Vladimir Reshetnikov, Sep 27 2016 *)
CROSSREFS
Sequence in context: A062020 A066183 A262297 * A026382 A054492 A128525
KEYWORD
easy,nonn
EXTENSIONS
Corrected and extended by T. D. Noe, Nov 07 2006
STATUS
approved