Search: id:A033951
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%I A033951
%S A033951 1,8,23,46,77,116,163,218,281,352,431,518,613,716,827,946,1073,1208,
%T A033951 1351,1502,1661,1828,2003,2186,2377,2576,2783,2998,3221,3452,3691,3938,
%U A033951 4193,4456,4727,5006,5293,5588,5891,6202,6521,6848,7183,7526,7877,8236
%N A033951 Write 1,2,... in clockwise spiral; sequence gives numbers on positive 
               x axis.
%H A033951 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A033951 a(n) = 4n^2+3n+1.
%F A033951 G.f.: (1+5x+2x^2)/(1-x)^3.
%F A033951 Equals A132774 * [1, 2, 3,...]; = binomial transform of [1, 7, 8, 0, 
               0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 28 2007
%F A033951 a(n)=8*n+a(n-1)-9 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 09 2009]
%e A033951 ... 16 5 6 7 22 ...
%e A033951 ... 15 4 1 8 23 ...
%e A033951 ... 14 3 2 9 24 ...
%e A033951 For n=2, a(2)=8*2+1-9=8; n=3, a(3)=8*3+8-9=23; n=4, a(4)=8*4+23-9=46 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
%t A033951 lst={};Do[p=4*n^2+3*n+1;AppendTo[lst, p], {n, 1, 6!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Sep 01 2008]
%o A033951 (PARI) a(n)=4*n^2+3*n+1
%Y A033951 Sequences from spirals: A001107, A002939, A007742, A033951, A033952, 
               A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
%Y A033951 A014848(2n+1)=a(n).
%Y A033951 Cf. A132774.
%Y A033951 a(n) = A016754(n) - n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 17 2009]
%Y A033951 Sequence in context: A164131 A114381 A139433 this_sequence A027054 A048467 
               A002765
%Y A033951 Adjacent sequences: A033948 A033949 A033950 this_sequence A033952 A033953 
               A033954
%K A033951 nonn,easy,nice,new
%O A033951 0,2
%A A033951 Olivier Gorin (gorin(AT)roazhon.inra.fr)
%E A033951 Extended (with formula) by Erich Friedman (erich.friedman(AT)stetson.edu).

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