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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(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

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Last modified June 25 11:55 EDT 2017. Contains 288710 sequences.