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

Author

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

Keywords

• nonn
• easy
• changed

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).

Crossrefs

Cf. A057078, A102283.

Programs

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

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 *)

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

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

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)

Extensions

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

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