A249604 a(n) = Sum_{i=1..n} Fibonacci(i)*10^(i-1).

1, 11, 211, 3211, 53211, 853211, 13853211, 223853211, 3623853211, 58623853211, 948623853211, 15348623853211, 248348623853211, 4018348623853211, 65018348623853211, 1052018348623853211, 17022018348623853211, 275422018348623853211, 4456422018348623853211

Offset: 1

Author

N. J. A. Sloane, Nov 04 2014

Keywords

• nonn
• easy

Examples

			To get a(10), for example:
..........1
.........1
........2
.......3
......5
.....8
...13
..21
.34
55
-----------
58623853211
		

References

• 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.

Links

• Colin Barker, Table of n, a(n) for n = 1..800
• Index entries for linear recurrences with constant coefficients, signature (11,90,-100).

Crossrefs

Cf. A000045, A000071.

The analog for powers of 2 is A064108.

Programs

PARI

Vec(x / ((1-x)*(1-10*x-100*x^2)) + O(x^30)) \\ Colin Barker, Jun 26 2017

Formula

O.g.f.: x/((1-x)*(1-10*x-100*x^2)). - Bruno Berselli, Nov 04 2014

From Colin Barker, Jun 26 2017: (Start)

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

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

(End)