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

Author

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

Keywords

• nonn
• easy

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]

Examples

			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
		

Links

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

Crossrefs

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

Programs

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 *)

Extensions

Edited by Georg Fischer, Dec 03 2024