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A088003
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Take the list t[n,0]={1,...,n}; denote by t[n,j] this list after rotating to left[or right] by j positions. Calculate inner product of t[n,0] and t[n,j] and denote the value by s[n,j]. Compute this inner product for all j=1,..,n and choose the smallest. This is a[n].
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3
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1, 4, 11, 22, 40, 64, 98, 140, 195, 260, 341, 434, 546, 672, 820, 984, 1173, 1380, 1615, 1870, 2156, 2464, 2806, 3172, 3575, 4004, 4473, 4970, 5510, 6080, 6696, 7344, 8041, 8772, 9555, 10374, 11248, 12160, 13130, 14140, 15211, 16324, 17501, 18722, 20010
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If instead of Min the Max was computed, then A000330(n), the square piramidal numbers was obtained. Also, inner product of t with 1-rotated-t is calculated, then A006527(n) is produced.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
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FORMULA
| a(n)=Min{y; y=t[n, 0]*t[n, x]=s[n, x]; for x=1, .., n}
a(n)=n*(2*n*(5*n+12)-3*(-1)^n+11)/48.
G. f.: x*(1+2x+2x^2)/((1+x)^2*(1-x)^4). - Bruno Berselli, Dec 01 2010
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EXAMPLE
| n=6: t[6,0]={1,2,3,4,5,6}, t[6,3]={4,5,6,1,2,3};
compute scalar products for all rotations:
{76,67,64,67,76,91} of which smallest is 64, so a[6]=64.
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MATHEMATICA
| t0[x_] := Table[w, {w, 1, x}]; jr[x_, j_] := RotateRight[t0[x], j]; Table[Min[Table[Apply[Plus, t0[g]*jr[g, i]], {i, 1, g}]], {g, 1, up}]
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CROSSREFS
| Cf. A000330, A006527.
Cf. A094414.
Sequence in context: A132072 A009846 A008043 * A049836 A177853 A008016
Adjacent sequences: A088000 A088001 A088002 * A088004 A088005 A088006
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 14 2003
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EXTENSIONS
| Edited by Bruno Berselli (berselli.bruno(AT)yahoo.it), Dec 01 2010
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