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A071764 Number of minimal rectangular envelopes (up to rotation) that enclose n contiguous squares. 1
1, 1, 1, 2, 3, 4, 6, 8, 11, 14, 17, 21, 26, 30, 36, 42, 48, 54, 62, 69, 78, 86, 95, 105, 116, 125, 136, 148, 160, 172, 186, 198, 213, 227, 242, 258, 274, 288, 306, 324, 342, 359, 379, 397, 418, 438, 458, 480, 503, 523, 546, 569, 593, 617, 643, 667, 693, 718, 745 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Equivalently, number of distinct envelopes up to rotation of the polyominoes of order n, n >= 0. - Francois Alcover, Feb 28 2017

LINKS

Table of n, a(n) for n=0..58.

K. S. Brown, More info

FORMULA

a(n) = (1/2)*( A000217(n) + A008619(n)- A000196(n-1) - A006218(n-1) ).

Recurrence : a(n) = a(n-1) + {n/2} - {tau(n-1)/2} where {x} signifies the least integer greater than or equal to x, tau(x) the number of divisors of x.

EXAMPLE

From Francois Alcover, Feb 28 2017: (Start)

a(3) = 2:

The two possible envelopes are

|*|

|*|

|*| [3,1]

and

|*| |

|*|*| [2,2] (End)

MATHEMATICA

a[0] = 1; a[n_] := (1/2)*(Floor[(n+1)/2] - Floor[Sqrt[n-1]] + n*(n+1)/2 - Sum[Floor[(n-1)/i], {i, 1, n}]); Table[a[n], {n, 0, 58}] (* Jean-Fran├žois Alcover, Feb 01 2018, from PARI *)

PROG

(PARI) for(n=1, 100, print1(1/2*(n*(n+1)/2+floor((n+1)/2)-floor(sqrt(n-1))-sum(i=1, n, floor((n-1)/i))), ", "))

CROSSREFS

Sequence in context: A242110 A056829 A211536 * A238381 A290743 A059291

Adjacent sequences:  A071761 A071762 A071763 * A071765 A071766 A071767

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Jun 04 2002

STATUS

approved

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)