cp's OEIS Frontend

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 ...

%I A161372 #7 Dec 03 2024 12:21:38
%S A161372 107,101,121,103,143,113,173,131,211,157,257,191,311,233,373,283,443,
%T A161372 341,521,407,607,481,701,563,803,653,913,751,1031,857,1157,971,1291,
%U A161372 1093,1433,1223,1583,1361,1741,1507,1907,1661,2081,1823,2263,1993,2453
%N 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 ...
%C A161372 NE to SW Diagonal of Ulam's Spiral, with 101 at center.
%C A161372 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]
%H A161372 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%e A161372 SW-NE diagonal in:
%e A161372   137 136 135 134 133 132 131
%e A161372   138 117 116 115 114 113 130
%e A161372   139 118 105 104 103 112 129
%e A161372   140 119 106 101 102 111 128
%e A161372   141 120 107 108 109 110 127
%e A161372   142 121 122 123 124 125 126
%e A161372   143 144 145 146 147 148 149
%t A161372 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 *)
%Y A161372 Cf. A054569 (SW spoke), A054554 (NE spoke).
%K A161372 nonn,easy
%O A161372 1,1
%A A161372 Milton L. Brown (miltbrown(AT)earthlink.net), Jun 08 2009
%E A161372 Edited by _Georg Fischer_, Dec 03 2024