A152890 -id:A152890 - cp's OEIS frontend

A170926 Total number of squares and rectangles at the n-th stage in the corner toothpick structure (see A152890, A153006).

0, 0, 1, 3, 4, 5, 10, 17, 20, 21, 25, 30, 33, 40, 58, 77, 84, 85, 89, 94, 97, 104, 121, 138, 145, 151, 164, 177, 190, 222, 278, 325, 340, 341, 345, 350, 353, 360, 377, 394, 401, 407, 420, 433, 446, 478, 533, 578, 593, 599, 612, 625, 638, 669, 720, 761, 781, 806, 845, 884, 942

Offset: 0

Omar E. Pol, Jan 18 2010

nonn

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

Partial sums of A168131.

a(2^k) = (4^k-4)/3 for k >= 2. - N. J. A. Sloane, Feb 13 2010.

Edited and extended by N. J. A. Sloane, Feb 01 2010

A026051 a(n) = (d(n)-r(n))/5, where d = A026049 and r is the periodic sequence with fundamental period (4,1,4,0,1).

Original entry on oeis.org

23, 31, 40, 53, 68, 86, 109, 135, 167, 203, 244, 292, 345, 406, 473, 547, 630, 720, 820, 928, 1045, 1173, 1310, 1459, 1618, 1788, 1971, 2165, 2373, 2593, 2826, 3074, 3335, 3612, 3903, 4209, 4532, 4870, 5226, 5598, 5987, 6395, 6820, 7265, 7728, 8210, 8713, 9235, 9779, 10343, 10928, 11536

Offset: 7

Clark Kimberling

nonn

A152890 [From Richard Choulet, Dec 14 2008]

a(n)=(n + 7)*(2*n^2 + 13*n + 102)/30 - 1/5*(2 + ( - 1/5*5^(1/2) + 1)*cos(2*n*Pi/5) + (2/5*2^(1/2)*(5 - 5^(1/2))^(1/2))*sin(2*n*Pi/5) + (1/5*5^(1/2) + 1)*cos(4*n*Pi/5) + ( - 2/5*2^(1/2)*(5 + 5^(1/2))^(1/2))*sin(4*n*Pi/5)) [From Richard Choulet, Dec 14 2008]

cp's OEIS Frontend

A170926 Total number of squares and rectangles at the n-th stage in the corner toothpick structure (see A152890, A153006).

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