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A131242 a(n) = Sum_{k=0..n} floor(k/10). (Partial sums of A059995.) 16
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

Table of n, a(n) for n=0..67.

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

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)

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

CROSSREFS

Cf. A059995, A010879, A002266, A130488.

Cf. Similar sequences: A000217, A002620, A130518, A130519, A130520, A174709, A174738, A118729, A218470.

Sequence in context: A164836 A005358 A032518 * A008728 A179052 A083292

Adjacent sequences:  A131239 A131240 A131241 * A131243 A131244 A131245

KEYWORD

nonn,easy

AUTHOR

Hieronymus Fischer, Jun 21 2007

STATUS

approved

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Last modified December 5 05:27 EST 2016. Contains 278761 sequences.