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URL: https://oeis.org/A218470

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A218470
Partial sums of floor(n/9).
16
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.
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 *)
LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, 70] (* Harvey P. Dale, Sep 14 2025 *)
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: A088380 A122620 A381964 * A008727 A357745 A088450
KEYWORD
nonn,tabf,easy
AUTHOR
Philippe Deléham, Mar 26 2013
STATUS
approved