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

0,3

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) = 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

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

Cf. A000217, A176271.

Sequence in context: A342661 A213821 A022157 * A171228 A328618 A318680

Adjacent sequences: A065596 A065597 A065598 * A065600 A065601 A065602

Keyword

nonn,easy,changed

Author

George E. Antoniou, Dec 01 2001

Status

approved