A081494 Start with Pascal's triangle; form a triangle by sliding down n steps from top on both sides and including the horizontal row, deleting the inner numbers; a(n) = sum of entries on perimeter of triangle.

1, 3, 7, 13, 23, 41, 75, 141, 271, 529, 1043, 2069, 4119, 8217, 16411, 32797, 65567, 131105, 262179, 524325, 1048615, 2097193, 4194347, 8388653, 16777263, 33554481, 67108915, 134217781, 268435511, 536870969, 1073741883, 2147483709

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

For n > 1, a(n) = A061761(n-1). - David Wasserman, Jun 03 2004

Example

The triangle pertaining to n = 4 is obtained from the solid triangle
        1
      1   1
    1   2   1
  1   3   3   1
giving
        1
      1   1
    1       1
  1   3   3   1
and the sum of all the numbers is 13, so a(4) = 13.

Maple

restart:a:= proc(n) option remember; if n=0 then 1 else add((binomial (n, j)+2), j=0..n-1) fi end: seq (a(n), n=0..31); # Zerinvary Lajos, Mar 29 2009

Crossrefs

Cf. A081495, A081496, A081497.

First differences of A290707.

Sequence in context: A066624 A317783 A061761 * A161909 A281131 A173168

Adjacent sequences: A081491 A081492 A081493 * A081495 A081496 A081497

Keyword

nonn

Author

Amarnath Murthy, Mar 25 2003

Extensions

Corrected and extended by David Wasserman, Jun 03 2004

Status

approved