A078344 - OEIS

A078344

a(1)=1; a(2)=2; a(3)=3; a(n) = Sum_{k=3..n-1} (a(k) + a(k-1) + a(k-2)).

1, 2, 3, 6, 17, 43, 109, 278, 708, 1803, 4592, 11695, 29785, 75857, 193194, 492030, 1253111, 3191446, 8128033, 20700623, 52720725, 134270106, 341961560, 870913951, 2218059568, 5648994647, 14386962813, 36640979841, 93317917142

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..29.

Index entries for linear recurrences with constant coefficients, signature (2,1,1).

FORMULA

a(n) is asymptotic to a*b^n where a = 0.1570450524507584150437292... and b is the real root of: x^3 - 2*x^2 - x - 1; b = 2.546818276884082079135997..

a(n) = 2*a(n-1)+a(n-2)+a(n-3) for n>4. G.f.: x*(3*x^3+2*x^2-1) / (x^3+x^2+2*x-1). - Colin Barker, Jun 24 2013

CROSSREFS

Sequence in context: A204514 A338594 A375565 * A392640 A024498 A319283

Adjacent sequences: A078341 A078342 A078343 * A078345 A078346 A078347

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Nov 22 2002

STATUS

approved