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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)