A249604 - OEIS

%I #20 Jun 26 2017 07:29:26

%S 1,11,211,3211,53211,853211,13853211,223853211,3623853211,58623853211,

%T 948623853211,15348623853211,248348623853211,4018348623853211,

%U 65018348623853211,1052018348623853211,17022018348623853211,275422018348623853211,4456422018348623853211

%N a(n) = Sum_{i=1..n} Fibonacci(i)*10^(i-1).

%D D. R. Kaprekar, Demlofication of Fibonacci numbers, Journal of University of Bombay, Nov. 1945. Reprinted in D. R. Kaprekar, Demlo Numbers, Privately printed, Khare's Wada, Deolali, India, 1948, pp. 75-82.

%H Colin Barker, <a href="/A249604/b249604.txt">Table of n, a(n) for n = 1..800</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,90,-100).

%F O.g.f.: x/((1-x)*(1-10*x-100*x^2)). - _Bruno Berselli_, Nov 04 2014

%F From _Colin Barker_, Jun 26 2017: (Start)

%F a(n) = ((-10 + (5-21*sqrt(5))*(5-5*sqrt(5))^n + (5*(1+sqrt(5)))^n*(5+21*sqrt(5)))) / 1090.

%F a(n) = 11*a(n-1) + 90*a(n-2) - 100*a(n-3) for n>3.

%F (End)

%e To get a(10), for example:

%e ..........1

%e .........1

%e ........2

%e .......3

%e ......5

%e .....8

%e ...13

%e ..21

%e .34

%e 55

%e -----------

%e 58623853211

%o (PARI) Vec(x / ((1-x)*(1-10*x-100*x^2)) + O(x^30)) \\ _Colin Barker_, Jun 26 2017

%Y Cf. A000045, A000071.

%Y The analog for powers of 2 is A064108.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Nov 04 2014