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%I #14 Feb 24 2021 02:48:18
%S 0,2,6,14,22,30,42,70,86,94,106,134,154,182,222,310,342,350,362,390,
%T 410,438,478,566,602,630,670,758,814,906,1046,1302,1366,1374,1386,
%U 1414,1434,1462,1502,1590,1626,1654,1694,1782,1838,1930,2070,2326,2394,2422,2462
%N Number of toothpicks in the toothpick structure A139250 that are orthogonal to the initial toothpick after n even rounds.
%C Also, partial sums of A162794.
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%p a139251 := BFILETOLIST("b139251.txt") ; A162794 := proc(n) global a139251; op(2*n,a139251) ; end: A162796 := proc(n) add( A162794(k),k=1..n) ; end: seq(A162796(n),n=1..120) ; # _R. J. Mathar_, Sep 27 2009
%t terms = 100;
%t Cases[Import["https://oeis.org/A139251/b139251.txt", "Table"], {_, _}][[;; 2terms;; 2, 2]] // Accumulate (* _Jean-François Alcover_, Mar 24 2020 *)
%Y Cf. A139250, A139251, A159791, A159792, A162793, A162794, A162795, A162797.
%K nonn
%O 0,2
%A _Omar E. Pol_, Jul 14 2009
%E Extended by _R. J. Mathar_, Sep 27 2009
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