A193744 Partial sum of Perrin numbers.

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

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