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A195149 Concentric 22-gonal numbers.

%I A195149 #37 Jun 19 2025 21:15:26
%S A195149 0,1,22,45,88,133,198,265,352,441,550,661,792,925,1078,1233,1408,1585,
%T A195149 1782,1981,2200,2421,2662,2905,3168,3433,3718,4005,4312,4621,4950,
%U A195149 5281,5632,5985,6358,6733,7128,7525,7942,8361,8800,9241,9702,10165,10648,11133
%N A195149 Concentric 22-gonal numbers.
%C A195149 Sequence found by reading the line from 0, in the direction 0, 22,..., and the same line from 1, in the direction 1, 45,..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Main axis, perpendicular to A152740 in the same spiral.
%H A195149 Vincenzo Librandi, <a href="/A195149/b195149.txt">Table of n, a(n) for n = 0..10000</a>
%H A195149 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A195149 G.f.: -x*(1+20*x+x^2) / ( (1+x)*(x-1)^3 ). - _R. J. Mathar_, Sep 18 2011
%F A195149 a(n) = (22*n^2+9*(-1)^n-9)/4; a(n) = -a(n-1)+11*n^2-11*n+1. - _Vincenzo Librandi_, Sep 27 2011
%F A195149 Sum_{n>=1} 1/a(n) = Pi^2/132 + tan(3*Pi/(2*sqrt(11)))*Pi/(6*sqrt(11)). - _Amiram Eldar_, Jan 17 2023
%F A195149 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). - _Wesley Ivan Hurt_, Jun 19 2025
%p A195149 A195149:=n->(22*n^2+9*(-1)^n-9)/4: seq(A195149(n), n=0..50); # _Wesley Ivan Hurt_, Jul 07 2014
%t A195149 Table[(22*n^2 + 9*(-1)^n - 9)/4, {n, 0, 50}] (* _Wesley Ivan Hurt_, Jul 07 2014 *)
%o A195149 (Magma) [(22*n^2+9*(-1)^n-9)/4: n in [0..50]]; // _Vincenzo Librandi_, Sep 27 2011
%o A195149 (PARI) a(n)=(22*n^2+9*(-1)^n-9)/4 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A195149 A195323 and A195318 interleaved.
%Y A195149 Cf. A032528, A077221, A195142, A195143, A195145, A195146, A195147, A195148.
%Y A195149 Cf. A032527, A195049, A195058. Column 22 of A195040. - _Omar E. Pol_, Sep 29 2011
%K A195149 nonn,easy
%O A195149 0,3
%A A195149 _Omar E. Pol_, Sep 17 2011