This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A220517 First differences of A225600. Also A141285 and A194446 interleaved. 17
 1, 1, 2, 2, 3, 3, 2, 1, 4, 5, 3, 1, 5, 7, 2, 1, 4, 2, 3, 1, 6, 11, 3, 1, 5, 2, 4, 1, 7, 15, 2, 1, 4, 2, 3, 1, 6, 4, 5, 1, 4, 1, 8, 22, 3, 1, 5, 2, 4, 1, 7, 4, 3, 1, 6, 2, 5, 1, 9, 30, 2, 1, 4, 2, 3, 1, 6, 4, 5, 1, 4, 1, 8, 7, 4, 1, 7, 2, 6, 1, 5, 1, 10, 42 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Number of toothpicks added at n-th stage to the toothpick structure (related to integer partitions) of A225600. LINKS N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS FORMULA a(2n-1) = A141285(n); a(2n) = A194446(n), n >= 1 EXAMPLE Written as an irregular triangle in which row n has length 2*A187219(n) we can see that the right border gives A000041 and the previous term of the last term in row n is n. 1,1; 2,2; 3,3; 2,1,4,5; 3,1,5,7; 2,1,4,2,3,1,6,11; 3,1,5,2,4,1,7,15; 2,1,4,2,3,1,6,4,5,1,4,1,8,22; 3,1,5,2,4,1,7,4,3,1,6,2,5,1,9,30; 2,1,4,2,3,1,6,4,5,1,4,1,8,7,4,1,7,2,6,1,5,1,10,42; . Illustration of the first seven rows of triangle as a minimalist diagram of regions of the set of partitions of 7: .      _ _ _ _ _ _ _ . 15   _ _ _ _      | .      _ _ _ _|_    | .      _ _ _    |   | .      _ _ _|_ _|_  | . 11   _ _ _      | | .      _ _ _|_    | | .      _ _    |   | | .      _ _|_ _|_  | | .  7   _ _ _    | | | .      _ _ _|_  | | | .  5   _ _    | | | | .      _ _|_  | | | | .  3   _ _  | | | | | .  2   _  | | | | | | .  1    | | | | | | | . .      1 2 3 4 5 6 7 . Also using the elements of this diagram we can draw a Dyck path in which the n-th odd-indexed segment has A141285(n) up-steps and the n-th even-indexed segment has A194446(n) down-steps. Note that the height of the n-th largest peak between two valleys at height 0 is also the partition number A000041(n). See below: . 7.................................. .                                 /\ 5....................            /  \                /\ .                   /\          /    \          /\  / 3..........        /  \        /      \        /  \/ 2.....    /\      /    \    /\/        \      / 1..  /\  /  \  /\/      \  /            \  /\/ 0 /\/  \/    \/          \/              \/ . 0,2,  6,   12,         24,             40... = A211978 .  1, 4,   9,       19,           33... = A179862 . CROSSREFS Cf. A000041, A006128, A135010, A138137, A141285, A179862, A186114, A186412, A187219, A194446, A206437, A211978, A220517, A225600, A225610. Sequence in context: A125585 A191860 A109973 * A271076 A087175 A188817 Adjacent sequences:  A220514 A220515 A220516 * A220518 A220519 A220520 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Feb 07 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 22 07:30 EDT 2019. Contains 323478 sequences. (Running on oeis4.)