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

1,2

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).

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)

Example

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

Prog

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

Crossrefs

Cf. A000045, A000071.

The analog for powers of 2 is A064108.

Sequence in context: A069613 A075858 A136307 * A038399 A053547 A053582

Adjacent sequences: A249601 A249602 A249603 * A249605 A249606 A249607

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 04 2014

Status

approved