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Search: id:A056107
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| A056107 |
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Third spoke of a hexagonal spiral. |
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+0
15
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| 1, 4, 13, 28, 49, 76, 109, 148, 193, 244, 301, 364, 433, 508, 589, 676, 769, 868, 973, 1084, 1201, 1324, 1453, 1588, 1729, 1876, 2029, 2188, 2353, 2524, 2701, 2884, 3073, 3268, 3469, 3676, 3889, 4108, 4333, 4564, 4801, 5044, 5293, 5548, 5809, 6076, 6349
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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
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REFERENCES
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E. J. Barbeau et al., Five Hundred Mathematical Challenges, Problem 444 pp. 42;195 MAA Washington DC 1995.
L. Moser, Solution to Problem E773, American Mathematical Monthly, Washington DC 1948
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LINKS
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H. Bottomley, Illustration of initial terms
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
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FORMULA
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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
a(n)={A000578(n+1) - A000578(n-1)}/2. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 29 2005
a(n) = A132111(n+1,n-1) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 10 2007
Equals binomial transform of [1, 3, 6, 0, 0, 0,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 03 2008
a(n)=6*n+a(n-1)-9 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
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EXAMPLE
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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]
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MAPLE
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with (combinat):seq((fibonacci(5, n)-n^4), n=0..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A002648 for primes in this sequence, A054552 for example of square (or octagonal) spiral spoke.
Sequence in context: A108753 A024970 A079430 this_sequence A155433 A155392 A155435
Adjacent sequences: A056104 A056105 A056106 this_sequence A056108 A056109 A056110
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KEYWORD
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easy,nonn,new
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 09 2000
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