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A247643 a(n) = ( 10*n*(n+1)+(2*n+1)*(-1)^n+7 )/8.

%I A247643 #40 Feb 01 2020 09:31:39
%S A247643 1,3,9,15,27,37,55,69,93,111,141,163,199,225,267,297,345,379,433,471,
%T A247643 531,573,639,685,757,807,885,939,1023,1081,1171,1233,1329,1395,1497,
%U A247643 1567,1675,1749,1863,1941,2061,2143,2269,2355,2487,2577,2715,2809,2953,3051
%N A247643 a(n) = ( 10*n*(n+1)+(2*n+1)*(-1)^n+7 )/8.
%C A247643 From _Paul Curtz_, Jan 01 2020: (Start)
%C A247643 In the following pentagonal spiral of odd numbers
%C A247643                      101
%C A247643                   99  61  63
%C A247643               97  59  31  33  65
%C A247643           95  57  29  11  13  35  67
%C A247643       93  55  27   9   1   3  15  37  69
%C A247643         91  53  25   7   5  17  39  71
%C A247643           89  51  23  21  19  41  73
%C A247643             87  49  47  45  43  75
%C A247643               85  83  81  79  77
%C A247643 the terms of this sequence appear on the x axis. A062786 and A172043 are in the spiral as well. (End)
%H A247643 Vincenzo Librandi, <a href="/A247643/b247643.txt">Table of n, a(n) for n = 0..1000</a>
%H A247643 Johann Cigler, <a href="http://arxiv.org/abs/1501.04750">Some remarks and conjectures related to lattice paths in strips along the x-axis</a>, arXiv:1501.04750 [math.CO], 2015-2016.
%H A247643 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A247643 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). - _Colin Barker_, Sep 25 2014
%F A247643 G.f.: -(x^4+2*x^3+4*x^2+2*x+1) / ((x-1)^3*(x+1)^2). - _Colin Barker_, Sep 25 2014
%F A247643 From _Paul Curtz_, Jan 01 2020: (Start)
%F A247643 a(n) = 1 + 2*A085787(n).
%F A247643 a(n+1) = a(n-1) + A090772(n+1). (End)
%F A247643 E.g.f.: (1/4)*((1 + x)*(4 + 5*x)*cosh(x) + (3 + x*(11 + 5*x))*sinh(x)). - _Stefano Spezia_, Jan 01 2020
%p A247643 f:=n->(10*n*(n+1)+(2*n+1)*(-1)^n+7)/8;
%t A247643 Table[(10 n (n + 1) + (2 n + 1) (-1)^n + 7)/8, {n, 0, 60}] (* _Vincenzo Librandi_, Sep 26 2014 *)
%o A247643 (PARI) Vec(-(x^4+2*x^3+4*x^2+2*x+1) / ((x-1)^3*(x+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 25 2014
%Y A247643 A diagonal of triangle in A247646.
%Y A247643 Cf. A005408, A062786, A085787, A090772, A172043.
%K A247643 nonn,easy
%O A247643 0,2
%A A247643 _N. J. A. Sloane_, Sep 23 2014
%E A247643 More terms from _Colin Barker_, Sep 25 2014