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A037156 10^n*(10^n+1)/2. 1
1, 55, 5050, 500500, 50005000, 5000050000, 500000500000, 50000005000000, 5000000050000000, 500000000500000000, 50000000005000000000, 5000000000050000000000, 500000000000500000000000 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..12.

Brian Hayes, Gauss's Day of Reckoning, American Scientist

Bill Johnson, The great Gauss summation trick

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)

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)

CROSSREFS

A subsequence of the triangular numbers A000217.

Sequence in context: A119081 A119051 A119083 * A116110 A060204 A231783

Adjacent sequences:  A037153 A037154 A037155 * A037157 A037158 A037159

KEYWORD

easy,nonn

AUTHOR

Marvin Ray Burns

EXTENSIONS

Corrected by T. D. Noe, Nov 07 2006

STATUS

approved

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Last modified December 16 09:34 EST 2018. Contains 318160 sequences. (Running on oeis4.)