A301696 Partial sums of A219529.

1, 6, 17, 33, 54, 81, 113, 150, 193, 241, 294, 353, 417, 486, 561, 641, 726, 817, 913, 1014, 1121, 1233, 1350, 1473, 1601, 1734, 1873, 2017, 2166, 2321, 2481, 2646, 2817, 2993, 3174, 3361, 3553, 3750, 3953, 4161, 4374, 4593, 4817, 5046, 5281, 5521, 5766

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

From Colin Barker, Mar 26 2018: (Start)

G.f.: (1 + x)^4 / ((1 - x)^3*(1 + x + x^2)).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>4. (End)

From G. C. Greubel, May 27 2020: (Start)

a(n) = (ChebyshevU(n, -1/2) - ChebyshevU(n-1, -1/2) + 8*(3*n*(n+1) +1))/9.

a(n) = ( A131713(n) + 8*A028896(n) + 8 )/9. (End)

Maple

A301696:= n-> (8*(3*n*(n+1) +1) + `mod`(n+2, 3) - `mod`(n+1, 3))/9;
seq(A301696(n), n=0..60); # G. C. Greubel, May 27 2020

Mathematica

Table[(Mod[n+2, 3] - Mod[n+1, 3] + 8*(3*n*(n+1) +1))/9, {n, 0, 60}] (* G. C. Greubel, May 27 2020 *)

Prog

(PARI) Vec((1 + x)^4 / ((1 - x)^3*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Mar 26 2018
(Sage) [(24*n*(n+1)+8 + (n+2)%3 - (n+1)%3 )/9 for n in (0..60)] # G. C. Greubel, May 27 2020

Crossrefs

Cf. A219529.

Sequence in context: A130051 A338894 A237658 * A301727 A038795 A216892

Adjacent sequences: A301693 A301694 A301695 * A301697 A301698 A301699

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 25 2018

Status

approved