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

Offset

0,2

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).

Formula

a(n)=2*a(n-1)+a(n-2)+4; a(0)=1, a(1)=6.

a(n)=[ {(5+3*sqrt(2))(1+sqrt(2)^n - (5-3*sqrt(2))(1-sqrt(2))^n}/2*sqrt(2) ]-2.

a(n)=3*a(n-1)-a(n-2)-a(n-3). G.f.: (1+3*x)/((1-x)*(1-2*x-x^2)). [Colin Barker, Sep 19 2012]

a(n) = 2*Pell(n) + 3*Pell(n+1) - 2, where Pell = A000129. - Vladimir Reshetnikov, Sep 27 2016

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

Cf. A000129, A048655.

Sequence in context: A062020 A066183 A262297 * A026382 A054492 A128525

Adjacent sequences: A048743 A048744 A048745 * A048747 A048748 A048749

Keyword

easy,nonn

Author

Barry E. Williams

Extensions

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

Status

approved