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

Author

Philippe Deléham, Mar 26 2013

Keywords

• nonn
• tabf
• easy

Comments

Apart from the initial zeros, the same as A008727.

Examples

			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....
...
		

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).

Crossrefs

Cf. similar sequences: A118729, A174109, A174738.

Programs

Magma

[&+[Floor(k/9): k in [0..n]]: n in [0..70]]; // Bruno Berselli, Mar 27 2013

Mathematica

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

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