A152973 -id:A152973 - cp's OEIS frontend

A152978 a(n) = A139251(n+2)/4 = A152968(n+1)/2.

1, 1, 1, 2, 3, 2, 1, 2, 3, 3, 4, 7, 8, 4, 1, 2, 3, 3, 4, 7, 8, 5, 4, 7, 9, 10, 15, 22, 20, 8, 1, 2, 3, 3, 4, 7, 8, 5, 4, 7, 9, 10, 15, 22, 20, 9, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23, 28, 35, 52, 64, 48, 16, 1, 2, 3, 3, 4, 7, 8, 5, 4, 7, 9, 10, 15, 22, 20, 9, 4, 7, 9, 10, 15, 22, 21, 14, 15, 23

Offset: 1

Omar E. Pol, Dec 16 2008, Dec 20 2008

Also, first differences of toothpick numbers A153000.

			If written as a triangle, begins:
.1,1;
.1,2,3,2;
.1,2,3,3,4,7,8,4;
.1,2,3,3,4,7,8,5,4,7,9,10,15,22,20,8;
....
Rows converge to A152980.
It appears that row sums give A004171. [From _Omar E. Pol_, May 25 2010]

David Applegate, The movie version
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

Cf. toothpick sequence A139250.
Cf. A139251, A139252, A139560, A152968, A152973.
Cf. A152980, A152998, A153000, A153001, A153003, A153004, A153006.
Cf. A004171. [From Omar E. Pol, May 25 2010]

G.f.: (1+x)*(Prod(1+x^(2^k-1)+2*x^(2^k),k=1..oo)-1)/(1+2*x). - N. J. A. Sloane, May 20 2009

More terms from Omar E. Pol, Jul 26 2009

A152979 Records in A152978.

Original entry on oeis.org

1, 2, 3, 4, 7, 8, 9, 10, 15, 22, 23, 28, 35, 52, 64, 65, 74, 91, 122, 168, 176, 177, 186, 239, 304, 412, 512, 513, 524, 527, 599, 782, 1020, 1336, 1488, 1489, 1500, 1575, 1980, 2584, 3376, 4160, 4161, 4172, 4174, 4247, 4275, 4653, 5010, 6544, 8544

Offset: 1

Omar E. Pol, Dec 23 2008

nonn

This sequence also gives the records in A152980. - Nathaniel Johnston, Apr 10 2011

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

Cf. A039251, A152768, A152968, A152973, A152978, A152998, A153000, A153006. Toothpick sequence: A139250.

a(16)-a(51) from Nathaniel Johnston, Apr 10 2011

A153838 Records in A153004.

Original entry on oeis.org

1, 3, 6, 9, 12, 21, 24, 27, 30, 45, 66, 69, 84, 105, 156, 192, 195, 222, 273, 366, 504, 528, 531, 558, 717, 912, 1236, 1536, 1539, 1572, 1581, 1797, 2346, 3060, 4008, 4464, 4467, 4500, 4725, 5940, 7752, 10128, 12480, 12483, 12516, 12522, 12741, 12825, 13959

Offset: 1

Omar E. Pol, Jan 02 2009

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

Cf. A139251, A152768, A152973, A152978, A152979, A152998, A153000, A153003, A153004. Toothpick sequence: A139250.

read("transforms3") : a139250 := BFILETOLIST("b139250.txt") : A139250 := proc(n) global a139250; op(n+1,a139250) ; end: A153003 := proc(n) if n =0 then 0; else 1+3/4*(A139250(n+1)-3) ; fi; end: A153004 := proc(n) A153003(n)-A153003(n-1) ; end: rec := -1 ; for n from 1 to 3000 do t := A153004(n) ; if t > rec then printf("%d,",t) ; rec := t; fi; od: # R. J. Mathar, Jul 13 2009

More terms from R. J. Mathar, Jul 13 2009

cp's OEIS Frontend

A152978 a(n) = A139251(n+2)/4 = A152968(n+1)/2.

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A152979 Records in A152978.

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A153838 Records in A153004.

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