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A037156
a(n) = 10^n*(10^n+1)/2.
6
1, 55, 5050, 500500, 50005000, 5000050000, 500000500000, 50000005000000, 5000000050000000, 500000000500000000, 50000000005000000000, 5000000000050000000000, 500000000000500000000000, 50000000000005000000000000, 5000000000000050000000000000
OFFSET
0,2
COMMENTS
Sum of first 10^n positive integers. - Omar E. Pol, May 03 2015
REFERENCES
C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 328.
LINKS
Brian Hayes, Gauss's Day of Reckoning, American Scientist
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
FORMULA
a(n) = A000533(n) * A093143(n). - Omar E. Pol, May 03 2015
From Chai Wah Wu, May 28 2016: (Start)
a(n) = 110*a(n-1) - 1000*a(n-2).
G.f.: (1 - 55*x)/((10*x - 1)*(100*x - 1)).
(End)
a(n) = sqrt(A038544(n)). - Bernard Schott, Jan 20 2022
EXAMPLE
From Omar E. Pol, May 03 2015: (Start)
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)
MATHEMATICA
LinearRecurrence[{110, -1000}, {1, 55}, 20] (* Harvey P. Dale, Oct 11 2023 *)
CROSSREFS
A subsequence of the triangular numbers A000217.
Cf. A038544.
Sequence in context: A119081 A119051 A119083 * A116110 A358044 A060204
KEYWORD
easy,nonn
EXTENSIONS
Corrected by T. D. Noe, Nov 07 2006
STATUS
approved