A274129 Sum of all numbers that appear when we interpret an ordered subset of [0,1,...,n] containing n as the digits, possibly larger than nine, of a base ten number, with the smallest element being the least significant.

11, 253, 4257, 63085, 872861, 11569833, 148920497, 1876301845, 23259261861, 284671240513, 3448396611737, 41419505367405, 493973128085261, 5855648668464793, 69053522207998977, 810643999691917765, 9478691806054675061, 110443295770481522673

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..950

Marko Riedel, Maple code to compute sequence by enumeration and from the generating function.

Math.Stackexchange.Com, Marko Riedel et al., Decreasing sequence numbers

Index entries for linear recurrences with constant coefficients, signature (24,-165,242).

Formula

a(n) = (10/9) * n * 11^n - (11/81) * (11^n-2^n).

G.f.: 11 * z * (1-z) / ((1-11z)^2 * (1-2z)).

a(n) = 24*a(n-1)-165*a(n-2)+242*a(n-3) for n>3. - Colin Barker, Jul 20 2016

Example

a(2) = 253 because 210+21+20+2 = 253.

Maple

A274129 := n -> 10/9*n*11^n - 11/81*(11^n-2^n);

Mathematica

CoefficientList[Series[11*x*(1 - x)/((1 - 11*x)^2*(1 - 2*x)), {x, 0, 100} ], x] (* G. C. Greubel, Jul 07 2016 *)

Prog

(PARI) Vec(11*x*(1-x)/((1-11*x)^2*(1-2*x)) + O(x^20)) \\ Colin Barker, Jul 20 2016

Crossrefs

Sequence in context: A190680 A377327 A089298 * A346896 A012154 A377424

Adjacent sequences: A274126 A274127 A274128 * A274130 A274131 A274132

Keyword

nonn,base,easy

Author

Marko Riedel, Jul 07 2016

Status

approved