A181427 a(n) = n + [n^2 if n is odd or n^3 if n is even].

2, 10, 12, 68, 30, 222, 56, 520, 90, 1010, 132, 1740, 182, 2758, 240, 4112, 306, 5850, 380, 8020, 462, 10670, 552, 13848, 650, 17602, 756, 21980, 870, 27030, 992, 32800, 1122, 39338, 1260, 46692, 1406, 54910, 1560, 64040, 1722, 74130, 1892, 85228, 2070

Offset: 1

Author

Dinesh Panchamia (dgpanchamia(AT)gmail.com), Oct 19 2010

Keywords

• nonn
• easy

Comments

a(2*k+1) = 2*A000384(k+1) (k in A001477). - Bruno Berselli, Oct 20 2010

Examples

			For n=5, 5+5^2=30 and n=6 6+6^3=222.
		

Links

• B. Berselli, Table of n, a(n) for n = 1..10000. [From _Bruno Berselli_, Oct 20 2010]
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Crossrefs

Cf. A002939, A034262, A065679.

Cf. A000384, A001477.

Programs

Mathematica

If[OddQ[ # ],#+#^2,#+#^3]&/@Range[50] (* Harvey P. Dale, Nov 03 2010 *)

Formula

a(n) = n + n^(2*(n mod 2)+3*(1-(n mod 2))).

a(n) = n + n^((5+(-1)^n)/2) = n*(1+A065679(n)).

G.f.: 2*x*(1+5*x+2x^2+14*x^3-3*x^4+5*x^5)/(1-x^2)^4.

a(n)-4*a(n-2)+6*a(n-4)-4*a(n-6)+a(n-8) = 0 for n>8.

a(2*n) = A034262(2*n). a(2*n+1) = A002939(n+1).

Extensions

Formulas and more terms from R. J. Mathar and Bruno Berselli, Oct 19 2010