A193867 Odd central polygonal numbers.

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

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(n-1)).

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

G.f.: -x*(x^2+1)*(x^2+6*x+1) / ( (1+x)^2*(x-1)^3 ). - R. J. Mathar, Aug 25 2011

From Colin Barker, Jan 27 2016: (Start)

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

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

a(n) = 2*n^2-3*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*(x-1)^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