A193867 - OEIS

%I #22 Jan 27 2016 07:44:10

%S 1,7,11,29,37,67,79,121,137,191,211,277,301,379,407,497,529,631,667,

%T 781,821,947,991,1129,1177,1327,1379,1541,1597,1771,1831,2017,2081,

%U 2279,2347,2557,2629,2851,2927,3161,3241,3487,3571,3829,3917,4187,4279

%N Odd central polygonal numbers.

%C Even triangular numbers plus 1.

%C Union of A188135 and A185438 without repetitions ( A188135 is a bisection of this sequence. Another bisection is A185438 but without its initial term).

%H Colin Barker, <a href="/A193867/b193867.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F a(n) = A000124(A014601(n-1)).

%F a(n) = 1 + A014494(n-1).

%F G.f.: -x*(x^2+1)*(x^2+6*x+1) / ( (1+x)^2*(x-1)^3 ). - _R. J. Mathar_, Aug 25 2011

%F From _Colin Barker_, Jan 27 2016: (Start)

%F a(n) = (4*n^2+2*(-1)^n*n-4*n-(-1)^n+3)/2.

%F a(n) = 2*n^2-n+1 for n even.

%F a(n) = 2*n^2-3*n+2 for n odd.

%F (End)

%t Select[Accumulate[Range[0,100]],EvenQ]+1 (* or *) LinearRecurrence[{1,2,-2,-1,1},{1,7,11,29,37},50] (* _Harvey P. Dale_, Nov 29 2014 *)

%o (PARI) Vec(-x*(x^2+1)*(x^2+6*x+1) / ((1+x)^2*(x-1)^3) + O(x^100)) \\ _Colin Barker_, Jan 27 2016

%Y Cf. A000124, A193868.

%K nonn,easy

%O 1,2

%A _Omar E. Pol_, Aug 15 2011