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 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 (list; graph; refs; listen; history; text; internal format)
 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). LINKS 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(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. 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 Jean-François Alcover and Paul Curtz, Jul 14 2017 STATUS approved

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Last modified January 27 22:53 EST 2022. Contains 350654 sequences. (Running on oeis4.)