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A247643 a(n) = ( 10*n*(n+1)+(2*n+1)*(-1)^n+7 )/8. 3
1, 3, 9, 15, 27, 37, 55, 69, 93, 111, 141, 163, 199, 225, 267, 297, 345, 379, 433, 471, 531, 573, 639, 685, 757, 807, 885, 939, 1023, 1081, 1171, 1233, 1329, 1395, 1497, 1567, 1675, 1749, 1863, 1941, 2061, 2143, 2269, 2355, 2487, 2577, 2715, 2809, 2953, 3051 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From Paul Curtz, Jan 01 2020: (Start)

In the following pentagonal spiral of odd numbers

                     101

                  99  61  63

              97  59  31  33  65

          95  57  29  11  13  35  67

      93  55  27   9   1   3  15  37  69

        91  53  25   7   5  17  39  71

          89  51  23  21  19  41  73

            87  49  47  45  43  75

              85  83  81  79  77

the terms of this sequence appear on the x axis. A062786 and A172043 are in the spiral as well. (End)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Johann Cigler, Some remarks and conjectures related to lattice paths in strips along the x-axis, arXiv:1501.04750 [math.CO], 2015-2016.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). - Colin Barker, Sep 25 2014

G.f.: -(x^4+2*x^3+4*x^2+2*x+1) / ((x-1)^3*(x+1)^2). - Colin Barker, Sep 25 2014

From Paul Curtz, Jan 01 2020: (Start)

a(n) = 1 + 2*A085787(n).

a(n+1) = a(n-1) + A090772(n+1). (End)

E.g.f.: (1/4)*((1 + x)*(4 + 5*x)*cosh(x) + (3 + x*(11 + 5*x))*sinh(x)). - Stefano Spezia, Jan 01 2020

MAPLE

f:=n->(10*n*(n+1)+(2*n+1)*(-1)^n+7)/8;

MATHEMATICA

Table[(10 n (n + 1) + (2 n + 1) (-1)^n + 7)/8, {n, 0, 60}] (* Vincenzo Librandi, Sep 26 2014 *)

PROG

(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

CROSSREFS

A diagonal of triangle in A247646.

Cf. A005408, A062786, A085787, A090772, A172043.

Sequence in context: A319316 A087031 A089632 * A287351 A256388 A082897

Adjacent sequences:  A247640 A247641 A247642 * A247644 A247645 A247646

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 23 2014

EXTENSIONS

More terms from Colin Barker, Sep 25 2014

STATUS

approved

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Last modified September 25 18:58 EDT 2020. Contains 337344 sequences. (Running on oeis4.)