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Search: id:A033996
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| A033996 |
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8 times triangular numbers. |
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+0
31
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| 0, 8, 24, 48, 80, 120, 168, 224, 288, 360, 440, 528, 624, 728, 840, 960, 1088, 1224, 1368, 1520, 1680, 1848, 2024, 2208, 2400, 2600, 2808, 3024, 3248, 3480, 3720, 3968, 4224, 4488, 4760, 5040, 5328, 5624, 5928, 6240, 6560, 6888, 7224, 7568, 7920, 8280
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Write 0,1,2,... in clockwise spiral; sequence gives numbers on one of 4 diagonals.
Also numbers of the form n^2-1 which are always divisible by 8. See link for proof. - Cino Hilliard (hillcino368(AT)gmail.com), Mar 02 2003
Also, least m>n such that T(m)*T(n) is a square and more precisely that of A055112(n). {T(n)=A000217(n)} - Lekraj Beedassy (blekraj(AT)yahoo.com), May 14 2004
Or, product of nth even number and nth even nonprime. - Juri-Stepan Gerasimov(2stepan(AT)rambler.ru), Jul 26 2009
Except for the first term, a(n)=8*n+a(n-1), (with a(1)=8) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
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REFERENCES
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Stuart M. Ellerstein, J. Recreational Math. 29 (3) 188, 1998.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd ed., 1994, p. 99.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Cino Hilliard, 8 divides n^2-1 .
Eric Weisstein's World of Mathematics, Knight's Tour Graph
Eric Weisstein's World of Mathematics, Hamiltonian Path
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FORMULA
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4n^2+4n. G.f.: A(x) = 8*x/(1-x)^3.
a(n)=A016754(n)-1=2*A046092(n)=4*A002378(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), May 25 2004
a(n)=A049598-A046092; a(n)=A124080-A002378. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 06 2007
a(n) = A000217(n)*8. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
a(n)=A005843(n)*A163300(n). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 26 2009]
a(n)=8*n+a(n-1)-8 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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EXAMPLE
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16 17 18 19 ...
15 4 5 6 ...
14 3 0 7 ...
13 2 1 8 ...
For n=2, a(2)=8*2+0-8=8; n=3, a(3)=8*3+8-8=24; n=4, a(4)=8*4+24-8=48 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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MAPLE
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[seq(8*binomial(n, 2), n=1..46)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2006
with(finance):seq(add(futurevalue( k, 3, 2), k=0..n)/2, n=0..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008
with(finance):seq(add(futurevalue(n, 1, 2), k=0..n), n=0..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +8; AppendTo[lst, s], {n, 0, 7!, 8}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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PROGRAM
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(PARI) nsqm1(n) = { forstep(x=1, n, 2, y = x*x-1; print1(y" ") ) }
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CROSSREFS
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Cf. A016754, A028896, A027468.
Sequences from spirals: A001107, A002939, A007742, A033951, A033952, A033953, A033954, A033989, A033990, A033991, A002943, A033996, A033988.
Cf. A028895, A046092, A045943, A002378, A028896, A024966.
Cf. A049598, A046092, A124080, A002378.
Cf. A000217. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
Sequence in context: A063403 A122812 A022763 this_sequence A146980 A028612 A068857
Adjacent sequences: A033993 A033994 A033995 this_sequence A033997 A033998 A033999
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Cino Hilliard (hillcino368(AT)gmail.com), Mar 02 2003
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