A048746 Partial sums of A048655.

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

Author

Barry E. Williams

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-1).

Crossrefs

Cf. A000129, A048655.

Programs

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 *)

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

Extensions

Corrected and extended by T. D. Noe, Nov 07 2006