

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
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OFFSET

0,2


COMMENTS

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


LINKS

Table of n, a(n) for n=0..50.
Index entries for linear recurrences with constant coefficients, signature (1,2,2,1,1).


FORMULA

a(n) = (n + 1)*(n  1 + (n mod 2)).
a(n) = n * A109613(n1) 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.: (13*x3*x^23*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, n1)*(n+1) \\ Charles R Greathouse IV, Jul 14 2017


CROSSREFS

After 1, subsequence of A035106, A198442 and A214297.
Cf. A000466, A002378, A093178, A109613, A114285, A124356, A193356, A289296.
Sequence in context: A154785 A090512 A076175 * A067780 A290168 A124486
Adjacent sequences: A289867 A289868 A289869 * A289871 A289872 A289873


KEYWORD

sign,easy


AUTHOR

JeanFrançois Alcover and Paul Curtz, Jul 14 2017


STATUS

approved



