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A131242 Partial sums of A059995: a(n) = sum_{k=0..n} floor(k/10). 18
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 156, 162, 168, 174, 180, 186, 192, 198 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,12
COMMENTS
Complementary with A130488 regarding triangular numbers, in that A130488(n)+10*a(n)=n(n+1)/2=A000217(n).
LINKS
FORMULA
a(n) = (1/2)*floor(n/10)*(2n-8-10*floor(n/10)).
a(n) = A059995(n)*(2n-8-10*A059995(n))/2.
a(n) = (1/2)*A059995(n)*(n-8+A010879(n)).
a(n) = (n-A010879(n))*(n+A010879(n)-8)/20.
G.f.: x^10/((1-x^10)(1-x)^2).
From Philippe Deléham, Mar 27 2013: (Start)
a(10n) = A051624(n).
a(10n+1) = A135706(n).
a(10n+2) = A147874(n+1).
a(10n+3) = 2*A005476(n).
a(10n+4) = A033429(n).
a(10n+5) = A202803(n).
a(10n+6) = A168668(n).
a(10n+7) = 2*A147875(n).
a(10n+8) = A135705(n).
a(10n+9) = A124080(n). (End)
a(n) = A008728(n-10) for n>= 10. - Georg Fischer, Nov 03 2018
EXAMPLE
As square array :
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
12, 14, 16, 18, 20, 22, 24, 26, 28, 30
33, 36, 39, 42, 45, 48, 51, 54, 57, 60
64, 68, 72, 76, 80, 84, 88, 92, 96, 100
105, 110, 115, 120, 125, 130, 135, 140, 145, 150
156, 162, 168, 174, 180, 186, 192, 198, 204, 210
... - Philippe Deléham, Mar 27 2013
MATHEMATICA
Table[(1/2)*Floor[n/10]*(2*n - 8 - 10*Floor[n/10]), {n, 0, 50}] (* G. C. Greubel, Dec 13 2016 *)
Accumulate[Table[FromDigits[Most[IntegerDigits[n]]], {n, 0, 110}]] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, 120] (* Harvey P. Dale, Apr 06 2017 *)
PROG
(PARI) for(n=0, 50, print1((1/2)*floor(n/10)*(2n-8-10*floor(n/10)), ", ")) \\ G. C. Greubel, Dec 13 2016
(PARI) a(n)=my(k=n\10); k*(n-5*k-4) \\ Charles R Greathouse IV, Dec 13 2016
CROSSREFS
Sequence in context: A164836 A005358 A032518 * A008728 A179052 A083292
KEYWORD
nonn,easy
AUTHOR
Hieronymus Fischer, Jun 21 2007
STATUS
approved

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Last modified May 18 11:53 EDT 2024. Contains 372630 sequences. (Running on oeis4.)