The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A180665 Golden Triangle sums: a(n)=a(n-2)+A001654(n) with a(0)=0 and a(1)=1. 6
 0, 1, 2, 7, 17, 47, 121, 320, 835, 2190, 5730, 15006, 39282, 102847, 269252, 704917, 1845491, 4831565, 12649195, 33116030, 86698885, 226980636, 594243012, 1555748412, 4073002212, 10663258237, 27916772486, 73087059235 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The a(n) are the Kn21, Kn22, Kn23, Fi2, and Ze2 sums of the Golden Triangle A180662. Furthermore the a(2*n) are the Kn3, Fi1 (terms doubled) and Ze3 (terms tripled) sums. See A180662 for information about these and other chess sums. LINKS Index entries for linear recurrences with constant coefficients, signature (2, 3, -3, -2, 1). FORMULA a(n) = a(n-2)+A001654(n) with a(0)=0 and a(1)=1. GF(x) = (-x)/((x-1)*(x+1)^2*(x^2-3*x+1)). a(n) = ((-1)^(-n-1)*(15+10*n)-25+(16-4*A)*A^(-n-1)+(16-4*B)*B^(-n-1))/100 with A=(3+sqrt(5))/2 and B=(3-sqrt(5))/2. MAPLE nmax:=27: with(combinat): for n from 0 to nmax do A001654(n):=fibonacci(n)*fibonacci(n+1) od: a(0):=0: a(1):=1: for n from 2 to nmax do a(n) := a(n-2) + A001654(n) od: seq(a(n), n=0..nmax); CROSSREFS Cf. A064831, A180664, A180665, A115730, A180666. Sequence in context: A178441 A014742 A085411 * A275209 A007049 A133407 Adjacent sequences:  A180662 A180663 A180664 * A180666 A180667 A180668 KEYWORD easy,nonn AUTHOR Johannes W. Meijer, Sep 21 2010 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 January 23 16:45 EST 2020. Contains 331172 sequences. (Running on oeis4.)