login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054552 a(n) = 4*n^2 - 3*n + 1. 30
1, 2, 11, 28, 53, 86, 127, 176, 233, 298, 371, 452, 541, 638, 743, 856, 977, 1106, 1243, 1388, 1541, 1702, 1871, 2048, 2233, 2426, 2627, 2836, 3053, 3278, 3511, 3752, 4001, 4258, 4523, 4796, 5077, 5366, 5663, 5968, 6281, 6602, 6931, 7268, 7613, 7966, 8327 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also indices in any spiral organized like A054551.

Equals binomial transform of [1, 1, 8, 0, 0, 0, ...]. - Gary W. Adamson, May 11 2008

Ulam's spiral (E spoke). - Robert G. Wilson v, Oct 31 2011

For n > 0: left edge of the triangle A033293. [Reinhard Zumkeller, Jan 18 2012]

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Robert G. Wilson v, Cover of the March 1964 issue of Scientific American

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: (1-x+8*x^2)/(1-x)^3.

a(n) = 8*n+a(n-1)-7 (with a(0)=1). [Vincenzo Librandi, Aug 07 2010]

a(0)=1, a(1)=2, a(2)=11, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). [Harvey P. Dale, Oct 10 2011]

EXAMPLE

The spiral begins:

197 196 195 194 193 192 191 190 189 188 187 186 185 184 183

198 145 144 143 142 141 140 139 138 137 136 135 134 133 182

199 146 101 100  99  98  97  96  95  94  93  92  91 132 181

200 147 102  65  64  63  62  61  60  59  58  57  90 131 180

201 148 103  66  37  36  35  34  33  32  31  56  89 130 179

202 149 104  67  38  17  16  15  14  13  30  55  88 129 178

203 150 105  68  39  18   5   4   3  12  29  54  87 128 177

204 151 106  69  40  19   6   1   2  11  28  53  86 127 176

205 152 107  70  41  20   7   8   9  10  27  52  85 126 175

206 153 108  71  42  21  22  23  24  25  26  51  84 125 174

207 154 109  72  43  44  45  46  47  48  49  50  83 124 173

208 155 110  73  74  75  76  77  78  79  80  81  82 123 172

209 156 111 112 113 114 115 116 117 118 119 120 121 122 171

210 157 158 159 160 161 162 163 164 165 166 167 168 169 170

211 212 213 214 215 216 217 218 219 220 221 222 223 224 225

- Robert G. Wilson v, Jul 04 2014

MAPLE

A054552:=n->4*n^2-3*n+1: seq(A054552(n), n=0..50); # Wesley Ivan Hurt, Jul 11 2014

MATHEMATICA

f[n_] := 4*n^2 - 3*n + 1; Array[f, 50, 0] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)

PROG

(PARI) a(n)= 4*n^2-3*n+1 \\ Charles R Greathouse IV, Jan 15 2012

(MAGMA) [4*n^2-3*n+1 : n in [0..50]]; // Wesley Ivan Hurt, Jul 11 2014

CROSSREFS

Cf. A054551, A108781.

Spokes of Ulam's spiral: A054552, A054554, A054556, A053755, A054567, A054569, A033951, A016754.

Sequence in context: A161527 A254196 A143651 * A277361 A034534 A220833

Adjacent sequences:  A054549 A054550 A054551 * A054553 A054554 A054555

KEYWORD

easy,nonn

AUTHOR

Enoch Haga and G. L. Honaker, Jr., Apr 09 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified July 23 22:27 EDT 2017. Contains 289716 sequences.