A159786 Total area of all squares and rectangles after n-th stage in the toothpick structure of A139250, assuming the toothpicks have length 2.

0, 0, 0, 4, 8, 8, 12, 32, 48, 48, 52, 64, 72, 76, 104, 176, 224, 224, 228, 240, 248, 252, 280, 336, 368, 372, 392, 424, 444, 480, 608, 864, 960, 960, 964, 976, 984, 988, 1016, 1072, 1104, 1108, 1128, 1160, 1180, 1216, 1344, 1536, 1632, 1636, 1656

Offset

0,4

Comments

Note that if n > 1 is a power of 2 then a(n) = n^2 - 2n.

Links

Table of n, a(n) for n=0..50.

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Formula

a(2^k) = A211012(k). - Omar E. Pol, Sep 25 2012

Crossrefs

Cf. A139250, A139251, A159787, A159788, A159789, A159796.

Sequence in context: A014198 A316316 A333288 * A083744 A255992 A273572

Adjacent sequences: A159783 A159784 A159785 * A159787 A159788 A159789

Keyword

nonn

Author

Omar E. Pol, Apr 28 2009

Extensions

More terms from Omar E. Pol, Sep 25 2012

Status

approved