A289296 a(n) = (n - 1)*(2*floor(n/2) + 1).

-1, 0, 3, 6, 15, 20, 35, 42, 63, 72, 99, 110, 143, 156, 195, 210, 255, 272, 323, 342, 399, 420, 483, 506, 575, 600, 675, 702, 783, 812, 899, 930, 1023, 1056, 1155, 1190, 1295, 1332, 1443, 1482, 1599, 1640, 1763, 1806, 1935, 1980, 2115, 2162, 2303, 2352, 2499, 2550, 2703, 2756, 2915

Offset

0,3

Comments

Summing a(n) by pairs, one gets -1, 9, 35, 77, 135, ... = A033566.

A198442(k) is a member of this sequence if k == 0 or 1 (mod 4). - Bruno Berselli, Jul 04 2017

Links

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

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

Formula

a(n) = A023443(n) * A109613(n).

a(n) = n^2-1 if n is even and n^2-n if n is odd.

n^2 - a(n) = A093178(n).

From Colin Barker, Jul 02 2017: (Start)

G.f.: -(1 - x - 5*x^2 - x^3 - 2*x^4) / ((1 - x)^3*(1 + x)^2).

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

Mathematica

Table[(n - 1) (2 Floor[n/2] + 1), {n, 0, 60}] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {-1, 0, 3, 6, 15}, 61]

Prog

(PARI) a(n)=(n\2*2+1)*(n-1) \\ Charles R Greathouse IV, Jul 02 2017
(PARI) Vec(-(1 - x - 5*x^2 - x^3 - 2*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^60)) \\ Colin Barker, Jul 02 2017
(Python)
def A289296(n): return (n-1)*(n|1) # Chai Wah Wu, Jan 18 2023

Crossrefs

Subsequence of A214297.

Cf. A023443, A033566, A093178, A109613.

Sequence in context: A342555 A075868 A162335 * A310126 A298015 A256906

Adjacent sequences: A289293 A289294 A289295 * A289297 A289298 A289299

Keyword

sign,easy

Author

Jean-François Alcover and Paul Curtz, Jul 02 2017

Status

approved