A036255 Number of inequivalent strings of 2n+1 digits, when 2 strings are equivalent if turning 1 upside down gives the other.

9, 945, 98475, 9961125, 999024375, 99975590625, 9999389671875, 999984741328125, 99999618530859375, 9999990463259765625, 999999761581435546875, 99999994039535595703125, 9999999850988388427734375, 999999996274709703369140625, 99999999906867742547607421875

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