login
A289870
a(n) = n*(n + 1) for n odd, otherwise a(n) = (n - 1)*(n + 1).
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
0,2
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).
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).
MATHEMATICA
a[n_] := (n + 1)(n - 1 + Mod[n, 2]); Table[a[n], {n, 0, 50}]
PROG
(PARI) a(n)=if(n%2, n, n-1)*(n+1) \\ Charles R Greathouse IV, Jul 14 2017
CROSSREFS
After -1, subsequence of A035106, A198442 and A214297.
Sequence in context: A374730 A090512 A076175 * A067780 A290168 A124486
KEYWORD
sign,easy
AUTHOR
STATUS
approved