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A033996
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8 times triangular numbers.
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36
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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 n-th even number and n-th even nonprime. - Juri-Stepan Gerasimov(2stepan(AT)rambler.ru), Jul 26 2009
Also sequence found by reading the line from 0, in the direction 0, 8,... and the same line from 0, in the direction 0, 24,..., in the square spiral whose vertices are the generalized decagonal numbers A074377. Axis perpendicular to A195146 in the same spiral. - Omar E. Pol, Sep 18 2011
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REFERENCES
| 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
| 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
| 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) = a(n-1)+8*n (with a(0)=0). [From Vincenzo Librandi, Nov 17 2010]
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EXAMPLE
| 16 17 18 19 ...
15 4 5 6 ...
14 3 0 7 ...
13 2 1 8 ...
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MAPLE
| [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
| 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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PROG
| (PARI) nsqm1(n) = { forstep(x=1, n, 2, y = x*x-1; print1(y" ") ) }
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CROSSREFS
| 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: A122812 A022763 A179682 * A146980 A028612 A068857
Adjacent sequences: A033993 A033994 A033995 * A033997 A033998 A033999
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Cino Hilliard (hillcino368(AT)gmail.com), Mar 02 2003
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