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A037156
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a(n) = 10^n*(10^n+1)/2.
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5
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1, 55, 5050, 500500, 50005000, 5000050000, 500000500000, 50000005000000, 5000000050000000, 500000000500000000, 50000000005000000000, 5000000000050000000000, 500000000000500000000000, 50000000000005000000000000, 5000000000000050000000000000
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listen;
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OFFSET
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0,2
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COMMENTS
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Sum of first 10^n positive integers. - Omar E. Pol, May 03 2015
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REFERENCES
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C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 328.
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LINKS
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C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
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FORMULA
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a(n) = 110*a(n-1) - 1000*a(n-2).
G.f.: (1 - 55*x)/((10*x - 1)*(100*x - 1)).
(End)
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EXAMPLE
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For n = 0; a(0) = 1 = 1 * 1 = 1
For n = 1; a(1) = 1 + 2 + ...... + 9 + 10 = 11 * 5 = 55
For n = 2; a(2) = 1 + 2 + .... + 99 + 100 = 101 * 50 = 5050
For n = 3; a(3) = 1 + 2 + .. + 999 + 1000 = 1001 * 500 = 500500
...
(End)
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MATHEMATICA
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LinearRecurrence[{110, -1000}, {1, 55}, 20] (* Harvey P. Dale, Oct 11 2023 *)
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CROSSREFS
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A subsequence of the triangular numbers A000217.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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