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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 August 3 10:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)