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Search: id:A035008
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| A035008 |
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Total number of possible knight moves on an n+2 X n+2 chessboard, if the knight is placed anywhere. |
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23
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| 0, 16, 48, 96, 160, 240, 336, 448, 576, 720, 880, 1056, 1248, 1456, 1680, 1920, 2176, 2448, 2736, 3040, 3360, 3696, 4048, 4416, 4800, 5200, 5616, 6048, 6496, 6960, 7440, 7936, 8448, 8976, 9520, 10080, 10656, 11248, 11856, 12480, 13120, 13776
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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16 times triangular numbers A000217.
Centered 16-gonal numbers A069129, minus 1. Also, sequence found by reading the segment (0, 16) together with the line from 16, in the direction 16, 48,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol (info(AT)polprimos.com), Apr 26 2008, Nov 20 2008
Number of n permutations (n>=2) of 5 objects u, v, z, x, y with repetition allowed, containing n-2 u's. Example: if n=2 then n-2 =zero (0) u, a(1)=16 because we have vv, zz, xx, yy, vz, zv, vx, xv, vy, yv, zx, xz, zy, yz, xy, yx., if n=3 then n-2=one (1) u, a(2)=48, if n=4 then n-2=two (2) u, a(3)= 96, etc. ... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 07 2008]
Except for the first term, a(n)=16*n+a(n-1), (with a(1)=16) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
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FORMULA
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a(n) = 8*n*(n+1). G.F.: A(x) = 16*x/(1-x)^3.
a(n) = A069129(n+1) - 1. - Omar E. Pol (info(AT)polprimos.com), Apr 26 2008
a(n)=C(n+1,2)*4^2, n>=0. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 07 2008]
a(n) = A000217(n)*16. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
a(n) = 8n^2 + 8n = A002378(n)*8 = A046092(n)*4 = A033996(n)*2. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
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EXAMPLE
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3 X 3-Board: knight can be placed in 8 positions with 2 moves from each, so a(1) = 16.
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MAPLE
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with(finance):seq(add(futurevalue( k, 3, 2), k=0..n), n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 15 2008
seq(binomial(n+1, 2)*4^2, n=0..33); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 07 2008]
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CROSSREFS
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Cf. A033586, A035006, A002492, A027468.
Cf. A000217, A069129.
A008586 A038231 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 07 2008]
Cf. A002378, A033996, A046092. [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
Sequence in context: A084112 A050428 A134605 this_sequence A023648 A098322 A109098
Adjacent sequences: A035005 A035006 A035007 this_sequence A035009 A035010 A035011
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu)
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