A321180 a(n) = 17*n^2 - 1.

-1, 16, 67, 152, 271, 424, 611, 832, 1087, 1376, 1699, 2056, 2447, 2872, 3331, 3824, 4351, 4912, 5507, 6136, 6799, 7496, 8227, 8992, 9791, 10624, 11491, 12392, 13327, 14296, 15299, 16336, 17407, 18512, 19651, 20824, 22031, 23272, 24547, 25856, 27199, 28576, 29987

Offset: 0

Author

Paul Curtz, Oct 29 2018

Keywords

• sign
• easy
• less

Comments

a(n) mod 9 = period 9: repeat [8, 7, 4, 8, 1, 1, 8, 4, 7] = A254375(n+5).

1020 = 2*2*15*17.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000079, A005408, A061085, A244630, A254375.

Programs

Mathematica

a[n_]:=17*n^2 - 1; Array[a, 50] (* or *)
CoefficientList[Series[(1 - 19 x - 16 x^2)/(-1 + x)^3, {x, 0, 50}], x] (* Stefano Spezia, Oct 29 2018 *)
LinearRecurrence[{3,-3,1},{-1,16,67},40] (* Harvey P. Dale, Jul 03 2021 *)

PARI

a(n)=17*n^2-1 \\ Charles R Greathouse IV, Oct 30 2018

PARI

Vec((1 - 19*x - 16*x^2)/(-1 + x)^3 + O(x^50)) \\ Colin Barker, Oct 31 2018

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

a(n) = A244630(n) - 1.

a(n+1) = a(n) + 17*(2n+1).

a(n+10) = a(n) + 10*A061085(n+5).

a(n+15) = a(15-n) + 1020*n.

G.f.: (1 - 19*x - 16*x^2)/(-1 + x)^3. - Stefano Spezia, Oct 29 2018

E.g.f.: exp(x)*(17*x^2 + 17*x - 1). - Elmo R. Oliveira, Jan 16 2025

Extensions

One term corrected by Colin Barker, Oct 29 2018