login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082652 Triangle read by rows: T(k,c) = number of squares that can be found in a c X k rectangular grid of little squares, for 1 <= c <= k. 5
1, 2, 5, 3, 8, 14, 4, 11, 20, 30, 5, 14, 26, 40, 55, 6, 17, 32, 50, 70, 91, 7, 20, 38, 60, 85, 112, 140, 8, 23, 44, 70, 100, 133, 168, 204, 9, 26, 50, 80, 115, 154, 196, 240, 285, 10, 29, 56, 90, 130, 175, 224, 276, 330, 385, 11, 32, 62, 100, 145, 196, 252, 312, 375, 440 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

T(k,c) also is the total number of balls in a pyramid of balls on a k X c rectangular base. - N. J. A. Sloane, Nov 17 2007. For example, if the base is 4 X 2, the total number of balls is 4*2 + 3*1 = 11 = T(4,2).

1

2 5

3 8 14

4 11 20 30

5 14 26 40 55

6 17 32 50 70 91

7 20 38 60 85 112 140

Here the squares being counted have sides parallel to the gridlines; for all squares, see A130684.

LINKS

Table of n, a(n) for n=1..65.

FORMULA

T(k, c) = ( c + 3*c*k + 3*c^2*k - c^3 ) / 6.

T(k, c) = Sum{ i = 0..min(k,c)} (k-i)*(c-i). - N. J. A. Sloane, Nov 17 2007

EXAMPLE

Let X represent a small square. Then T(3,2) = 8 because here

XXX

XXX

we can see 8 squares, 6 of side 1, 2 of side 2.

MAPLE

f:=proc(m, n) add((m-i)*(n-i), i=0..min(m, n)); end;

CROSSREFS

Cf. A083003, A083487. Right side of triangle gives A000330.

Main diagonal is A000330, row sums are A001296. - Paul D. Hanna and other correspondents, May 28 2003

Cf. A130684. - Joel B. Lewis

Sequence in context: A261927 A262870 A244418 * A194007 A065222 A159988

Adjacent sequences:  A082649 A082650 A082651 * A082653 A082654 A082655

KEYWORD

nonn,tabl

AUTHOR

Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), May 16 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified July 21 04:27 EDT 2017. Contains 289632 sequences.