%I A056108
%S A056108 1,5,15,31,53,81,115,155,201,253,311,375,445,521,603,691,785,885,991,
%T A056108 1103,1221,1345,1475,1611,1753,1901,2055,2215,2381,2553,2731,2915,3105,
%U A056108 3301,3503,3711,3925,4145,4371,4603,4841,5085,5335,5591,5853,6121,6395
%N A056108 Fourth spoke of a hexagonal spiral.
%C A056108 If Y is a 4-subset of an n-set X then, for n>=4, a(n-4) is the number 
               of 4-subsets of X having at least two elements in common with Y. 
               - Milan R. Janjic (agnus(AT)blic.net), Dec 08 2007
%C A056108 a(n) = A096777(3*n+1) . - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 29 2007
%C A056108 Comment from A. K. Devaraj (dkandadai(AT)yahoo.com), Sep 18 2009: (Start)
%C A056108 Let f(x) be a polynomial in x. Then f(x + n*f(x)) is congruent to 0 (mod(f(x)); 
               here n belongs to N.
%C A056108 There is nothing interesting in the quotients f(x + n*f(x))/f(x) when 
               x belongs to Z.
%C A056108 However, when x is irrational these quotients consist of two parts, a) 
               rational integers and b) integer multiples of x.
%C A056108 The present sequence is the integer part when the polynomial is x^2 + 
               x + 1 and x = sqrt(2),
%C A056108 f(x+n*f(x))/f(x) = a(n) + A005563(n)*sqrt(2).
%C A056108 (End)
%H A056108 H. Bottomley, <a href="a3215.gif">Illustration of initial terms</a>
%H A056108 G. Nebe and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               lattices/A2.html">Home page for hexagonal (or triangular) lattice 
               A2</a>
%F A056108 a(n) = 3n^2+n+1 = a(n-1)+6n-2 = 2a(n-1)-a(n-2)+6 = 3a(n-1)-3a(n-2)+a(n-3) 
               = A056105(n)+3n = A056106(n)+2n = A056107(n)+n = A056109(n)-n = A003215(n)-2n
%F A056108 a(n) = sum of (n+1)-th row terms of triangle A134234.= - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Oct 14 2007
%F A056108 Equals binomial transform of [1, 4, 6, 0, 0, 0,...] - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Apr 30 2008
%F A056108 a(n)=6*n+a(n-1)-8 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 09 2009]
%e A056108 For n=2, a(2)=6*2+1-8=5; n=3, a(3)=6*3+5-8=15; n=4, a(4)=6*4+15-8=31 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
%t A056108 s = 1; lst = {s}; Do[s += n + 3; AppendTo[lst, s], {n, 1, 300, 6}]; lst 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
%Y A056108 Cf. A054552 for example of square (or octagonal) spiral spoke.
%Y A056108 Cf. A134234.
%Y A056108 A000217 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
%Y A056108 Sequence in context: A048065 A048021 A133268 this_sequence A055831 A037984 
               A073361
%Y A056108 Adjacent sequences: A056105 A056106 A056107 this_sequence A056109 A056110 
               A056111
%K A056108 easy,nonn,new
%O A056108 0,2
%A A056108 Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000