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A004799 Self convolution of Lucas numbers 1,3,4,7,... 9
1, 6, 17, 38, 80, 158, 303, 566, 1039, 1880, 3364, 5964, 10493, 18342, 31885, 55162, 95032, 163114, 279051, 475990, 809771, 1374316, 2327372, 3933528, 6636025, 11176518, 18794633, 31560206, 52925984, 88646390, 148303719, 247841654 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

É. Czabarka, R. Flórez, L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.

FORMULA

a(n) = A060922(n, 1) (second column of Lucas triangle). a(n) = ((-4+5*n)*L(n+1) + 2*L(n))/5 with L(n) = A000032(n) = A000204(n), n >= 1. G.f.: x*((1+2*x)/(1-x-x^2))^2. - Wolfdieter Lang, Apr 24 2001

MAPLE

a:= n-> (Matrix([[17, 6, 1, 0]]). Matrix(4, (i, j)-> if i=j-1 then 1 elif j=1 then [2, 1, -2, -1][i] else 0 fi)^n) [1, 4]: seq (a(n), n=1..40); # Alois P. Heinz, Oct 28 2008

MATHEMATICA

a[n_] := ((5*n-4)*LucasL[n+1] + 2*LucasL[n])/5; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Nov 12 2015 *)

PROG

(PARI) Vec(x*((1+2*x)/(1-x-x^2))^2 + O(x^50)) \\ Altug Alkan, Nov 12 2015

(MAGMA) [((5*n-4)*Lucas(n+1) + 2*Lucas(n))/5: n in [1..30]]; // G. C. Greubel, Dec 17 2017

CROSSREFS

Cf. A000204.

Sequence in context: A023621 A000385 A192756 * A085278 A080275 A061349

Adjacent sequences:  A004796 A004797 A004798 * A004800 A004801 A004802

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Alois P. Heinz, Oct 28 2008

STATUS

approved

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Last modified January 23 01:37 EST 2021. Contains 340384 sequences. (Running on oeis4.)