A289870 a(n) = n*(n + 1) for n odd, otherwise a(n) = (n - 1)*(n + 1).

-1, 2, 3, 12, 15, 30, 35, 56, 63, 90, 99, 132, 143, 182, 195, 240, 255, 306, 323, 380, 399, 462, 483, 552, 575, 650, 675, 756, 783, 870, 899, 992, 1023, 1122, 1155, 1260, 1295, 1406, 1443, 1560, 1599, 1722, 1763, 1892, 1935, 2070, 2115, 2256, 2303, 2450, 2499

Offset: 0

Author

Jean-François Alcover and Paul Curtz, Jul 14 2017

Keywords

• sign
• easy

Comments

a(n) is a fifth-order linear recurrence whose main interest is that it is related to (at least) eight other sequences (see the formula section).

Links

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

Crossrefs

After -1, subsequence of A035106, A198442 and A214297.

Cf. A000466, A002378, A093178, A109613, A114285, A124356, A193356, A289296.

Programs

Mathematica

a[n_] := (n + 1)(n - 1 + Mod[n, 2]); Table[a[n], {n, 0, 50}]

PARI

a(n)=if(n%2, n, n-1)*(n+1) \\ Charles R Greathouse IV, Jul 14 2017

Formula

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

a(n) = n * A109613(n-1) for n>0.

a(n) = -A114285(n) * A109613(n).

a(n) = A002378(n) - A193356(n).

a(n) = A289296(-n).

a(n) = n^2 - (-1)^n * A093178(n).

a(2*k) = A000466(k).

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