cp's OEIS Frontend

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

%I A181427 #18 Feb 10 2025 05:49:57
%S A181427 2,10,12,68,30,222,56,520,90,1010,132,1740,182,2758,240,4112,306,5850,
%T A181427 380,8020,462,10670,552,13848,650,17602,756,21980,870,27030,992,32800,
%U A181427 1122,39338,1260,46692,1406,54910,1560,64040,1722,74130,1892,85228,2070
%N A181427 a(n) = n + [n^2 if n is odd or n^3 if n is even].
%C A181427 a(2*k+1) = 2*A000384(k+1) (k in A001477). - _Bruno Berselli_, Oct 20 2010
%H A181427 B. Berselli, <a href="/A181427/b181427.txt">Table of n, a(n) for n = 1..10000</a>. [From _Bruno Berselli_, Oct 20 2010]
%H A181427 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1).
%F A181427 a(n) = n + n^(2*(n mod 2)+3*(1-(n mod 2))).
%F A181427 a(n) = n + n^((5+(-1)^n)/2) = n*(1+A065679(n)).
%F A181427 G.f.: 2*x*(1+5*x+2x^2+14*x^3-3*x^4+5*x^5)/(1-x^2)^4.
%F A181427 a(n)-4*a(n-2)+6*a(n-4)-4*a(n-6)+a(n-8) = 0 for n>8.
%F A181427 a(2*n) = A034262(2*n). a(2*n+1) = A002939(n+1).
%e A181427 For n=5, 5+5^2=30 and n=6 6+6^3=222.
%t A181427 If[OddQ[ # ],#+#^2,#+#^3]&/@Range[50] (* _Harvey P. Dale_, Nov 03 2010 *)
%Y A181427 Cf. A002939, A034262, A065679.
%Y A181427 Cf. A000384, A001477.
%K A181427 nonn,easy
%O A181427 1,1
%A A181427 Dinesh Panchamia (dgpanchamia(AT)gmail.com), Oct 19 2010
%E A181427 Formulas and more terms from _R. J. Mathar_ and _Bruno Berselli_, Oct 19 2010