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A060531 a(n)=18a(n-1)-80a(n-2), a(0)=1, a(1)=9. G.f.: (1-9x)/((1-8x)(1-10x)). E.g.f. exp(9x)cosh(x). a(n)=8^n/2+10^n/2. 7
1, 9, 82, 756, 7048, 66384, 631072, 6048576, 58388608, 567108864, 5536870912, 54294967296, 534359738368, 5274877906944, 52199023255552, 517592186044416, 5140737488355328, 51125899906842624, 509007199254740992 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A081190. 9th binomial transform of (1,0,1,0,1,......), A059841.

Number of strings of n decimal digits that contain an even number of 0's. E.g. For n = 1 there are 9 strings: {1 2 3 4 5 6 7 8 9}; for n = 2 there are 82: {00 11 12 13 14 15 16 17 18 19 21 ... 96 97 98 99}.

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,200

Index entries for linear recurrences with constant coefficients, signature (18,-80).

FORMULA

a(1)=9, a(n) = 8*a(n-1) + 10^(n-1).

MAPLE

A060531 := proc(n) option remember: if n = 1 then RETURN(9) fi: 8*A060531(n-1) + 10^(n-1): end: for n from 1 to 40 do printf(`%d, `, A060531(n)) od:

PROG

(PARI) { for (n=0, 200, if (n==0, a=1, a=8*a + 10^(n - 1)); write("b060531.txt", n, " ", a); ) } [From Harry J. Smith, Jul 06 2009]

CROSSREFS

Cf. A081192.

Sequence in context: A068109 A163460 A081191 * A248848 A045741 A110567

Adjacent sequences:  A060528 A060529 A060530 * A060532 A060533 A060534

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 12 2001

EXTENSIONS

Additional comments from Paul Barry, Mar 11 2003

Typo in definition corrected by Paolo P. Lava, Sep 18 2008

STATUS

approved

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Last modified March 30 20:18 EDT 2017. Contains 284302 sequences.