This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A059633 G.f.: x^3/(1 - 2*x + x^3 - x^4). Recurrence: a(n) = 2*a(n-1) - a(n-3) + a(n-4). 7
 1, 2, 4, 7, 13, 24, 45, 84, 157, 293, 547, 1021, 1906, 3558, 6642, 12399, 23146, 43208, 80659, 150571, 281080, 524709, 979506, 1828503, 3413377, 6371957, 11894917, 22204960, 41451340, 77379720, 144449397, 269652414 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS Index entries for linear recurrences with constant coefficients, signature (2,0,-1,1). FORMULA Recurrence equations (A059633 is L(n)): I(n + 1) = I(n) + J(n) + L(n); J(n + 1) = I(n); K(n + 1) = J(n) + K(n); L(n + 1) = K(n); M(n + 1) = L(n) + 2M(n); initial conditions: I(0) = 1; J(0) = 0; K(0) = 0; L(0) = 0; M(0) = 0. Values for n = 0 1 2 3 4 5 6 7 8 ...: I(n) = 1 1 2 3 6 11 21 39 73 ... J(n) = 0 1 1 2 3 6 11 21 39 ... K(n) = 0 0 1 2 4 7 13 24 45 ... L(n) = 0 0 0 1 2 4 7 13 24 ... M(n) = 0 0 0 0 1 4 12 31 75 ... a(n) = A049856(n+2) - A049856(n+1) - A049856(n) + A049856(n-1). For n >= 2, a(n+1) = Sum_{i=0..n} Fibonacci(i)*binomial(n-i, i). - Benoit Cloitre, Sep 21 2004 a(n) = Sum_{k=0..n+1} C(k+1, n-k+1)F(n-k+1) [offset 0]. - Paul Barry, Feb 23 2005 MAPLE with(combstruct): SeqSeqSeqL := [T, {T=Sequence(S), S=Sequence(U, card > 1), U=Sequence(Z, card >1)}, unlabeled]: seq(count(SeqSeqSeqL, size=j), j=4..35); # Zerinvary Lajos, Apr 04 2009 CROSSREFS I and J are A049856 while K and L are A059633 (with some offsets). Sequence in context: A102111 A224704 A265826 * A088353 A192654 A260668 Adjacent sequences:  A059630 A059631 A059632 * A059634 A059635 A059636 KEYWORD nonn,easy AUTHOR James R. FitzSimons (cherry(AT)neta.com), Feb 19 2001 EXTENSIONS Comments and more terms from Henry Bottomley, Feb 21 2001 New description from Vladeta Jovovic, Jan 17 2004 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 December 10 16:44 EST 2018. Contains 318049 sequences. (Running on oeis4.)