

A193867


Odd central polygonal numbers.


5



1, 7, 11, 29, 37, 67, 79, 121, 137, 191, 211, 277, 301, 379, 407, 497, 529, 631, 667, 781, 821, 947, 991, 1129, 1177, 1327, 1379, 1541, 1597, 1771, 1831, 2017, 2081, 2279, 2347, 2557, 2629, 2851, 2927, 3161, 3241, 3487, 3571, 3829, 3917, 4187, 4279
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Even triangular numbers plus 1.
Union of A188135 and A185438 without repetitions ( A188135 is a bisection of this sequence. Another bisection is A185438 but without its initial term).


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,2,1,1).


FORMULA

a(n) = A000124(A014601(n1)).
a(n) = 1 + A014494(n1).
G.f.: x*(x^2+1)*(x^2+6*x+1) / ( (1+x)^2*(x1)^3 ).  R. J. Mathar, Aug 25 2011
From Colin Barker, Jan 27 2016: (Start)
a(n) = (4*n^2+2*(1)^n*n4*n(1)^n+3)/2.
a(n) = 2*n^2n+1 for n even.
a(n) = 2*n^23*n+2 for n odd.
(End)


MATHEMATICA

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 *)


PROG

(PARI) Vec(x*(x^2+1)*(x^2+6*x+1) / ((1+x)^2*(x1)^3) + O(x^100)) \\ Colin Barker, Jan 27 2016


CROSSREFS

Cf. A000124, A193868.
Sequence in context: A076304 A122560 A136338 * A110572 A023254 A129807
Adjacent sequences: A193864 A193865 A193866 * A193868 A193869 A193870


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Aug 15 2011


STATUS

approved



