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A118729 Infinite square array which contains the 8 numbers 4*r^2 - 3*r, 4*r^2 - 2*r, ..., 4*r^2 + 4*r in row r. 14
0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 42, 45, 48, 52, 56, 60, 64, 68, 72, 76, 80, 85, 90, 95, 100, 105, 110, 115, 120, 126, 132, 138, 144, 150, 156, 162, 168 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

The numbers in row r span the interval ]8*A000217(r-1), 8*A000217(r)].

The first difference between the entries in row r is r.

Partial sums of floor(n/8). - Philippe Deléham, Mar 26 2013

Apart from the initial zeros, the same as A008726. - Philippe Deléham, Mar 28 2013

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, 1, -2, 1).

FORMULA

From Philippe Deléham, Mar 26 2013: (Start)

a(8k)   = A001107(k).

a(8k+1) = A002939(k).

a(8k+2) = A033991(k).

a(8k+3) = A016742(k).

a(8k+4) = A007742(k).

a(8k+5) = A002943(k).

a(8k+6) = A033954(k).

a(8k+7) = A033996(k). (End)

G.f.: x^8/(((1-x)^2*(1-x^8)). - Philippe Deléham, Mar 28 2013

EXAMPLE

The array starts in row r=0 as

.0..0..0..0..0..0..0..0;

.1..2..3..4..5..6..7..8;

10.12.14.16.18.20.22.24;

27.30.33.36.39.42.45.48;

MATHEMATICA

Flatten[Table[4r^2+r(Range[-3, 4]), {r, 0, 6}]] (* or *) LinearRecurrence[ {2, -1, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, 60] (* Harvey P. Dale, Nov 26 2015 *)

CROSSREFS

Cf. similar sequences: A000217, A002620, A130518, A130519, A130520, A174709, A174738, A218470, A131242.

Sequence in context: A080750 A113768 A122936 * A008726 A302834 A022788

Adjacent sequences:  A118726 A118727 A118728 * A118730 A118731 A118732

KEYWORD

nonn,tabf,easy

AUTHOR

Stuart M. Ellerstein (ellerstein(AT)aol.com), May 21 2006

EXTENSIONS

Redefined as a square tabf array and description simplified by R. J. Mathar, Oct 20 2010

STATUS

approved

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Last modified October 21 13:05 EDT 2018. Contains 316422 sequences. (Running on oeis4.)