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A002477 Wonderful Demlo numbers: a(n) = ((10^(n+1)-1)/9)^2 = A000042^2.
(Formerly M5386 N2339)
+0
19
1, 121, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321, 1234567900987654321, 123456790120987654321, 12345679012320987654321, 1234567901234320987654321 (list; graph; listen)
OFFSET

1,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

D. R. Kaprekar, On Wonderful Demlo numbers, Math. Stud., 6 (1938), 68.

LINKS

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Repunit

FORMULA

G.f.: x*(1+10*x) / ((1-x)*(1-10*x)*(1-100*x)).

G.f.:sage: taylor( mul( x*(1+10*x) / ((1-x)*(1-10*x)*(1-100*x)) for i in xrange(1,2)),x,0,23)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]

MAPLE

A002477:=-(1+10*z)/(z-1)/(100*z-1)/(10*z-1); [S. Plouffe in his 1992 dissertation.]

MATHEMATICA

lst={}; Do[p=((10^n-1)/9)^2; AppendTo[lst, p], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 28 2008]

PROGRAM

(Other) sage: [gaussian_binomial(n, 1, 10)^2 for n in xrange(1, 14)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]

CROSSREFS

Cf. A002275.

Adjacent sequences: A002474 A002475 A002476 this_sequence A002478 A002479 A002480

Sequence in context: A137466 A062689 A057139 this_sequence A068117 A080162 A030174

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

Minor edits from N. J. A. Sloane (njas(AT)research.att.com), Aug 18 2009

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Last modified November 8 20:39 EST 2009. Contains 166234 sequences.


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