login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014832 a(1)=1; for n>1, a(n) = 9*a(n-1)+n. 3
1, 11, 102, 922, 8303, 74733, 672604, 6053444, 54481005, 490329055, 4412961506, 39716653566, 357449882107, 3217048938977, 28953440450808, 260580964057288, 2345228676515609, 21107058088640499 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..18.

Index entries for linear recurrences with constant coefficients, signature (11, -19, 9).

FORMULA

a(n) = (9^(n+1)-8*n-9)/64. - Rolf Pleisch, Oct 22 2010

a(1)=1, a(2)=11, a(3)=102; for n>3, a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3). - Harvey P. Dale, May 01 2012

G.f.: -(1/((x-1)^2*(9*x-1))). - Harvey P. Dale, May 01 2012

a(n) = Sum_{i=0..n-1} 8^i*binomial(n+1,n-1-i). [Bruno Berselli, Nov 13 2015]

EXAMPLE

For n=5, a(5) = 1*15 + 8*20 + 8^2*15 + 8^3*6 + 8^4*1 = 8303. [Bruno Berselli, Nov 13 2015]

MAPLE

a:=n->sum((9^(n-j)-1)/8, j=0..n): seq(a(n), n=1..18); # Zerinvary Lajos, Jan 15 2007

a:= n-> (Matrix([[1, 0, 1], [1, 1, 1], [0, 0, 9]])^n)[2, 3]: seq(a(n), n=1..18); # Alois P. Heinz, Aug 06 2008

MATHEMATICA

RecurrenceTable[{a[1]==1, a[n]==9a[n-1]+n}, a, {n, 20}] (* or *) LinearRecurrence[ {11, -19, 9}, {1, 11, 102}, 20] (* Harvey P. Dale, May 01 2012 *)

CROSSREFS

Cf. A001018, A104712.

Sequence in context: A037700 A037609 A055150 * A048441 A099294 A081552

Adjacent sequences:  A014829 A014830 A014831 * A014833 A014834 A014835

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)