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Search: id:A109965
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| A109965 |
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Sum_i {i<n} floor[sqrt(a(i))] with a(0) = 1. |
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+0
2
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| 1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 20, 24, 28, 33, 38, 44, 50, 57, 64, 72, 80, 88, 97, 106, 116, 126, 137, 148, 160, 172, 185, 198, 212, 226, 241, 256, 272, 288, 304, 321, 338, 356, 374, 393, 412, 432, 452, 473, 494, 516, 538, 561, 584, 608, 632, 657, 682, 708, 734
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The recursion to generate this sequence (excluding the additional extra 1 at the outset) occurs in Chapter 3, Exercise 28, page 97 in Graham, Knuth and Patashnik, Concrete Mathematics, 2nd Edition, Addison Wesley, 1994. A solution is provided on page 509. - Steve Tanny (tanny(AT)math.utoronto.ca), Apr 02 2008
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FORMULA
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a(n) = a(n-1)+floor[sqrt(a(n-1))] = a(n-1)+A109964(n-1) for n>1.
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EXAMPLE
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a(5) = floor[sqrt(1)] + floor[sqrt(1)] + floor[sqrt(2)] + floor[sqrt(3)] + floor[sqrt(4)] = 1 + 1 + 1 + 1 + 2 = 6.
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CROSSREFS
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Essentially the same as A002984.
Cf. A109964.
Sequence in context: A089649 A049700 A002984 this_sequence A008669 A055104 A062435
Adjacent sequences: A109962 A109963 A109964 this_sequence A109966 A109967 A109968
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jul 06 2005
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