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A301696
Partial sums of A219529.
3
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
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 25 2018
STATUS
approved