OFFSET
0,3
COMMENTS
a(n) = ABS(alternating sum of n-th row of the triangle in A176271), n>0. [Reinhard Zumkeller, Apr 13 2010]
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
FORMULA
a(n) = n^( n (mod 2) + 1 ).
O.g.f.: (x + 2*x^2 + 6*x^3 - 2*x^4 + x^5)/(1 - x^2)^3. - Len Smiley, Dec 04 2001
a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). - Wesley Ivan Hurt, Apr 26 2021
a(n) = n*((n+1)-(n-1)*(-1)^n)/2. - Aaron J Grech, Sep 03 2024
E.g.f.: x*(cosh(x) + (1 + x)*sinh(x)). - Stefano Spezia, Sep 26 2024
MATHEMATICA
Table[ n^(Mod[n, 2] + 1), {n, 1, 60} ]
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 1, 2, 9, 4, 25}, 80] (* Harvey P. Dale, Sep 10 2017 *)
PROG
(PARI) { for (n = 0, 1000, if (n%2, a=n^2, a=n); write("b065599.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 23 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
George E. Antoniou, Dec 01 2001
STATUS
approved