A218470 Partial sums of floor(n/9).

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 141, 147, 153, 159, 165, 171, 177, 183, 189, 196, 203, 210, 217, 224

Offset

0,11

Comments

Apart from the initial zeros, the same as A008727.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,1,-2,1).

Formula

a(9n) = A051682(n).

a(9n+1) = A062708(n).

a(9n+2) = A062741(n).

a(9n+3) = A022266(n).

a(9n+4) = A022267(n).

a(9n+5) = A081266(n).

a(9n+6) = A062725(n).

a(9n+7) = A062728(n).

a(9n+8) = A027468(n).

G.f.: x^9/((1-x)^2*(1-x^9)). - Bruno Berselli, Mar 27 2013

Example

As square array:
..0....0....0....0....0....0....0....0....0....
..1....2....3....4....5....6....7....8....9....
.11...13...15...17...19...21...23...25...27....
.30...33...36...39...42...45...48...51...54....
.58...62...66...70...74...78...82...86...90....
.95..100..105..110..115..120..125..130..135....
141..147..153..159..165..171..177..183..189....
196..203..210..217..224..231..238..245..252....
...

Mathematica

Accumulate[Floor[Range[0, 100]/9]] (* Jean-François Alcover, Mar 27 2013 *)

Prog

(Magma) [&+[Floor(k/9): k in [0..n]]: n in [0..70]]; // Bruno Berselli, Mar 27 2013
(PARI) for(n=0, 50, print1(sum(k=0, n, floor(k/9)), ", ")) \\ G. C. Greubel, Dec 13 2016
(PARI) a(n)=my(k=n\9); k*(9*k-7)/2 + k*(n-9*k) \\ Charles R Greathouse IV, Dec 13 2016

Crossrefs

Cf. similar sequences: A118729, A174109, A174738.

Sequence in context: A033061 A088380 A122620 * A008727 A357745 A088450

Adjacent sequences: A218467 A218468 A218469 * A218471 A218472 A218473

Keyword

nonn,tabf,easy

Author

Philippe Deléham, Mar 26 2013

Status

approved