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 A193744 Partial sum of Perrin numbers. 0
 3, 3, 5, 8, 10, 15, 20, 27, 37, 49, 66, 88, 117, 156, 207, 275, 365, 484, 642, 851, 1128, 1495, 1981, 2625, 3478, 4608, 6105, 8088, 10715, 14195, 18805, 24912, 33002, 43719, 57916, 76723, 101637, 134641, 178362, 236280, 313005, 414644, 549287, 727651, 963933, 1276940, 1691586 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Table of n, a(n) for n=0..46. Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1). FORMULA a(n)=Perrin(n+5)-2 a(n)=r1^(n+5)+r2^(n+5)+r3^(n+5)-2, where r1, r2, r3 are three roots of x^3-x-1=0. G.f.: (3 - x^2)/(1 - x^2 - x^3)/(1-x) = (3 - x^2) / (1 - x - x^2 + x^4). a(n) = a(n-1) + a(n-2) - a(n-4) for n > 2. - Franklin T. Adams-Watters, Aug 05 2011. EXAMPLE For n=2, a(2)=Perrin(0)+Perrin(1)+Perrin(2)=3+0+2=5. MAPLE perrin[0]:=3: perrin[1]:=0: perrin[2]:=2: a[0]:=3: a[1]:=3: a[2]:=5: for n from 0 to 100 do perrin[n]:=perrin[n-2]+perrin[n-3]: a[n]:=a[n-1]+perrin[n]: end do; MATHEMATICA LinearRecurrence[{0, 1, 1}, {3, 0, 2}, {6, 52}] - 2 (* Alonso del Arte, Aug 05 2011, based on Harvey P. Dale's program for A001608 *) LinearRecurrence[{1, 1, 0, -1}, {3, 3, 5, 8}, 47] (* Ray Chandler, Aug 03 2015 *) CROSSREFS Cf. A001608. Sequence in context: A177739 A323581 A327731 * A039872 A079965 A285069 Adjacent sequences: A193741 A193742 A193743 * A193745 A193746 A193747 KEYWORD nonn,easy AUTHOR Francesco Daddi, Aug 04 2011 STATUS approved

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Last modified September 9 20:10 EDT 2024. Contains 375765 sequences. (Running on oeis4.)