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A036255 Number of inequivalent strings of 2n+1 digits, when 2 strings are equivalent if turning 1 upside down gives the other. 3
9, 945, 98475, 9961125, 999024375, 99975590625, 9999389671875, 999984741328125, 99999618530859375, 9999990463259765625, 999999761581435546875, 99999994039535595703125, 9999999850988388427734375, 999999996274709703369140625, 99999999906867742547607421875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

De Bruijn, Polya's theory of counting, in Beckenbach, ed., Applied Combinatorial Math., Wiley, 1964 (p. 182).

LINKS

Colin Barker, Table of n, a(n) for n = 0..450

Index entries for linear recurrences with constant coefficients, signature (130,-3125,12500).

FORMULA

a(n) = 10^(2*n+1) - 5^(2*n+1)/2 + 3*5^n/2.

From Colin Barker, Jul 03 2017: (Start)

G.f.: 3*(3 - 75*x + 1250*x^2) / ((1 - 5*x)*(1 - 25*x)*(1 - 100*x)).

a(n) = 130*a(n-1) - 3125*a(n-2) + 12500*a(n-3) for n>2.

(End)

PROG

(PARI) Vec(3*(3 - 75*x + 1250*x^2) / ((1 - 5*x)*(1 - 25*x)*(1 - 100*x)) + O(x^20)) \\ Colin Barker, Jul 03 2017

CROSSREFS

Cf. A036257, A036258.

Sequence in context: A015107 A024124 A316535 * A070233 A087590 A048561

Adjacent sequences: A036252 A036253 A036254 * A036256 A036257 A036258

KEYWORD

nonn,easy,base

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 3 12:24 EST 2023. Contains 360035 sequences. (Running on oeis4.)