Search: id:A056107
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%I A056107
%S A056107 1,4,13,28,49,76,109,148,193,244,301,364,433,508,589,676,769,868,973,
%T A056107 1084,1201,1324,1453,1588,1729,1876,2029,2188,2353,2524,2701,2884,3073,
%U A056107 3268,3469,3676,3889,4108,4333,4564,4801,5044,5293,5548,5809,6076,6349
%N A056107 Third spoke of a hexagonal spiral.
%C A056107 a(n+1) is the number of lines crossing n cells of an n X n X n cube. 
               - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 29 2005
%D A056107 E. J. Barbeau et al., Five Hundred Mathematical Challenges, Problem 444 
               pp. 42;195 MAA Washington DC 1995.
%D A056107 L. Moser, Solution to Problem E773, American Mathematical Monthly, Washington 
               DC 1948
%H A056107 H. Bottomley, <a href="a3215.gif">Illustration of initial terms</a>
%H A056107 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 A056107 a(n) = 3n^2+1 = a(n-1)+6n-3 = 2a(n-1)-a(n-2)+6 = 3a(n-1)-3a(n-2)+a(n-3) 
               = A056105(n)+2n = A056106(n)+n = A056108(n)-n = A056109(n)-2n = A003215(n)-3n
%F A056107 a(n)={A000578(n+1) - A000578(n-1)}/2. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jul 29 2005
%F A056107 a(n) = A132111(n+1,n-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 10 2007
%F A056107 Equals binomial transform of [1, 3, 6, 0, 0, 0,...] - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), May 03 2008
%F A056107 a(n)=6*n+a(n-1)-9 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 09 2009]
%e A056107 For n=2, a(2)=6*2+1-9=4; n=3, a(3)=6*3+4-9=13; n=4, a(4)=6*4+13-9=28 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
%p A056107 with (combinat):seq((fibonacci(5, n)-n^4), n=0..46); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 07 2008
%t A056107 s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 275, 6}]; lst 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
%Y A056107 Cf. A002648 for primes in this sequence, A054552 for example of square 
               (or octagonal) spiral spoke.
%Y A056107 Sequence in context: A108753 A024970 A079430 this_sequence A155433 A155392 
               A155435
%Y A056107 Adjacent sequences: A056104 A056105 A056106 this_sequence A056108 A056109 
               A056110
%K A056107 easy,nonn
%O A056107 0,2
%A A056107 Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000

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