|
| |
|
|
A014824
|
|
a(0) = 0, a(n) = 10*a(n-1) + n.
|
|
16
| |
|
|
0, 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 1234567900, 12345679011, 123456790122, 1234567901233, 12345679012344, 123456790123455, 1234567901234566, 12345679012345677
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| The square roots of these numbers have some remarkable properties - see the link to Schizophrenic numbers.
Partial sums of A002275. [From Jonathan Vos Post, Apr 25 2010]
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
K. S. Brown, Schizophrenic numbers
Index entries for sequences related to linear recurrences with constant coefficients, signature (12,-21,10).
|
|
|
FORMULA
| a(n) =(10^n-1)*(10/81)-n/9 - Henry Bottomley, Jul 04 2000
a(n)/10^n converges to 10/81=0.123456790123456790...
Let b(n)=if(n=0, 1, if(n=1, 10, 10*9^(n-2))). Then a(n)=sum{k=0..n, C(n, k)b(k)} (Binomial transform) - Paul Barry, Jan 29 2004
G.f.: x/(1-12*x+21*x^2-10*x^3). [Colin Barker, Jan 08 2012]
|
|
|
MAPLE
| a:=n->sum((10^(n-j)-1^(n-j))/9, j=0..n): seq(a(n), n=0..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 15 2007
a:=n->sum(10^(n-j)*j, j=0..n): seq(a(n), n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2008
|
|
|
MATHEMATICA
| Table[Sum[10^i - 1, {i, n}]/9, {n, 18}] (from Robert G. Wilson v Nov 20 2004)
|
|
|
PROG
| (MAGMA) [(10^n-1)*(10/81)-n/9: n in [0..20]]; // Vincenzo Librandi, Aug 23 2011
|
|
|
CROSSREFS
| Cf. A007908, A060011.
Cf. A002275. [From Jonathan Vos Post, Apr 25 2010]
Sequence in context: A037610 A035239 A057137 * A060555 A138957 A007908
Adjacent sequences: A014821 A014822 A014823 * A014825 A014826 A014827
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
