A161372 In Ulam's spiral starting at 101, take the elements not used so far from the two spokes SW, NE, SW, NE, SW, NE ...

107, 101, 121, 103, 143, 113, 173, 131, 211, 157, 257, 191, 311, 233, 373, 283, 443, 341, 521, 407, 607, 481, 701, 563, 803, 653, 913, 751, 1031, 857, 1157, 971, 1291, 1093, 1433, 1223, 1583, 1361, 1741, 1507, 1907, 1661, 2081, 1823, 2263, 1993, 2453

Offset

1,1

Comments

NE to SW Diagonal of Ulam's Spiral, with 101 at center.

The sequence did not match the original definition. A working definition might be a(2n)=4n^2-10n+107, a(2n-1)=4n^2+2n+101, a(n)=n^2-n+105+2*(-1)^n*(1-2*n), but this seems to be unrelated to Ulam spirals. [R. J. Mathar, Jun 11 2009]

Links

Table of n, a(n) for n=1..47.

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

Example

SW-NE diagonal in:
  137 136 135 134 133 132 131
  138 117 116 115 114 113 130
  139 118 105 104 103 112 129
  140 119 106 101 102 111 128
  141 120 107 108 109 110 127
  142 121 122 123 124 125 126
  143 144 145 146 147 148 149

Mathematica

CoefficientList[Series[(107*x^4-6*x^3-194*x^2-6*x+107)/((1+x)^2*(1-x)^3), {x, 0, 32}], x] (* Georg Fischer, Dec 03 2024 *)

Crossrefs

Cf. A054569 (SW spoke), A054554 (NE spoke).

Sequence in context: A178546 A096712 A161176 * A099652 A344803 A294744

Adjacent sequences: A161369 A161370 A161371 * A161373 A161374 A161375

Keyword

nonn,easy,changed

Author

Milton L. Brown (miltbrown(AT)earthlink.net), Jun 08 2009

Extensions

Edited by Georg Fischer, Dec 03 2024

Status

approved