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A188378 Partial sums of A005248. 4
2, 5, 12, 30, 77, 200, 522, 1365, 3572, 9350, 24477, 64080, 167762, 439205, 1149852, 3010350, 7881197, 20633240, 54018522, 141422325, 370248452, 969323030, 2537720637, 6643838880, 17393796002, 45537549125, 119218851372, 312119004990, 817138163597, 2139295485800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Different from A024851.

LINKS

Robert Israel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4,1)

FORMULA

a(n) = A002878(n)+1 = 2*A027941(n+1)-3*A027941(n).

G.f. ( -2+3*x ) / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Mar 30 2011

a(n) = 5*A001654(n) + 1 + (-1)^n, n>=0. [Wolfdieter Lang, Jul 23 2012]

(a(n)^3 + (a(n)-2)^3) / 2 = A000032(A016945(n)) = Lucas(6n+3) = A267797(n), for n>0. - Altug Alkan, Jan 31 2016

a(n) = 2^(-1-n)*(2^(1+n)-(3-sqrt(5))^n*(-1+sqrt(5))+(1+sqrt(5))*(3+sqrt(5))^n). - Colin Barker, Nov 02 2016

MAPLE

f:= gfun:-rectoproc({a(n+3)-4*a(n+2)+4*a(n+1)-a(n), a(0) = 2, a(1) = 5, a(2) = 12}, a(n), remember):

map(f, [$0..60]); # Robert Israel, Feb 02 2016

MATHEMATICA

LinearRecurrence[{4, -4, 1}, {2, 5, 12}, 30] (* Harvey P. Dale, Oct 05 2015 *)

Accumulate@ LucasL@ Range[0, 58, 2] (* Michael De Vlieger, Jan 24 2016 *)

PROG

(PARI) a(n) = 5*fibonacci(n)*fibonacci(n+1) + 1 + (-1)^n; \\ Michel Marcus, Aug 26 2013

(PARI) Vec((-2+3*x)/((x-1)*(x^2-3*x+1)) + O(x^100)) \\ Altug Alkan, Jan 24 2016

(MAGMA) [5*Fibonacci(n)*Fibonacci(n+1)+1+(-1)^n: n in [0..40]]; // Vincenzo Librandi, Jan 24 2016

CROSSREFS

Cf. A267797. - Altug Alkan, Jan 31 2016

Sequence in context: A086622 A253831 A024851 * A145267 A103287 A136704

Adjacent sequences:  A188375 A188376 A188377 * A188379 A188380 A188381

KEYWORD

nonn,easy

AUTHOR

Gabriele Fici, Mar 29 2011

STATUS

approved

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Last modified July 19 08:23 EDT 2019. Contains 325155 sequences. (Running on oeis4.)