A065599 If n odd, a(n) = n^2 else a(n) = n.

0, 1, 2, 9, 4, 25, 6, 49, 8, 81, 10, 121, 12, 169, 14, 225, 16, 289, 18, 361, 20, 441, 22, 529, 24, 625, 26, 729, 28, 841, 30, 961, 32, 1089, 34, 1225, 36, 1369, 38, 1521, 40, 1681, 42, 1849, 44, 2025, 46, 2209, 48, 2401, 50, 2601, 52, 2809, 54, 3025, 56, 3249

Offset: 0

Author

George E. Antoniou, Dec 01 2001

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000217, A176271.

Programs

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 *)

PARI

a(n) = { if (n%2, n^2, n) } \\ Harry J. Smith, Oct 23 2009

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) = A000217(n)-(-1)^n*A000217(n-1) with A000217(-1)=0. - Bruno Berselli, Jun 07 2013

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