A131640 First differences are periodic: 50, 50, 75, 50, 50, 75, ...

985, 1035, 1085, 1160, 1210, 1260, 1335, 1385, 1435, 1510, 1560, 1610, 1685, 1735, 1785, 1860, 1910, 1960, 2035, 2085, 2135, 2210, 2260, 2310, 2385, 2435, 2485, 2560, 2610, 2660, 2735, 2785, 2835, 2910, 2960, 3010, 3085, 3135, 3185, 3260, 3310, 3360

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

G.f.: 5*(197 + 10*x + 10*x^2 - 182*x^3)/((1-x)^2*(1+x+x^2)). - R. J. Mathar, Nov 14 2007

From G. C. Greubel, Sep 08 2025: (Start)

a(n) = (5/3)*(35*(n+1) + 551 + 5*(A102283(n+1) + A102283(n))).

a(n) = (5/3)*(35*n + 586 + 5*A057078(n)).

E.g.f.: (5/3)*( 5*exp(-x/2)*( cos((sqrt(3)*x)/2) + (1/sqrt(3))*sin((sqrt(3)*x)/2)) + (586 + 35*x)*exp(x) ). (End)

Maple

A131640 := proc(n) option remember ; if n =0 then 985 ; elif n mod 3 = 0 then A131640(n-1)+75 ; else A131640(n-1)+50 ; fi ; end: seq(A131640(n), n=0..80) ; # R. J. Mathar, Oct 24 2007

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {985, 1035, 1085, 1160}, 50] (* Ray Chandler, Aug 25 2015 *)
Table[5*(35*n +591 -5*Mod[n, 3])/3, {n, 0, 50}] (* G. C. Greubel, Sep 08 2025 *)

Prog

(PARI) Vec(5*(197+10*x+10*x^2-182*x^3)/((1-x)^2*(1+x+x^2)) + O(x^40)) \\ Andrew Howroyd, Feb 20 2018
(Magma)
A131640:= func< n | (5/3)*(35*n + 591 - 5*(n mod 3) ) >;
[A131640(n): n in [0..50]]; // G. C. Greubel, Sep 08 2025
(SageMath)
def A131640(n): return 5*(35*n + 591 - 5*(n%3))//3
print([A131640(n) for n in range(51)]) # G. C. Greubel, Sep 08 2025

Crossrefs

Cf. A057078, A102283.

Sequence in context: A294183 A288840 A289417 * A333443 A183718 A163025

Adjacent sequences: A131637 A131638 A131639 * A131641 A131642 A131643

Keyword

nonn,easy

Author

Eric M. Adler (eadler(AT)simi.k12.ca.us), Sep 05 2007

Extensions

Definition supplied by N. J. A. Sloane, Sep 14 2007

More terms from R. J. Mathar, Oct 24 2007

Status

approved