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!)
 A132262 First term in a sum partition of the even-indexed Fibonacci numbers. 3
 1, 2, 7, 29, 130, 611, 2965, 14726, 74443, 381617, 1978582, 10355303, 54628201, 290148890, 1550177791, 8324934533, 44911554826, 243274479131, 1322555721037, 7213659006350, 39462884371891, 216470673634217, 1190382865461742, 6560913758341199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is the number in the center of the 3-regular tree when the exceptional representations of the 3-Kronecker quiver, whose dimension vector is given by subsequent even-indexed Fibonacci numbers are drawn into the 3-regular tree (the universal cover of the quiver). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Ph. Fahr and C. M. Ringel, A Partition Formula for Fibonacci Numbers, preprint, 2007. Ph. Fahr and C. M. Ringel, A Partition Formula for Fibonacci Numbers, Journal of Integer Sequences, Vol. 11 (2008), Article 08.1.4 Philipp Fahr and Claus Michael Ringel, Categorification of the Fibonacci Numbers Using Representations of Quivers, Journal of Integer Sequences, Vol. 15 (2012), Article 12.2.1 Michael D. Hirschhorn, On Recurrences of Fahr and Ringel Arising in Graph Theory, Journal of Integer Sequences, Vol. 12 (2009), Article 09.6.8 Harris Kwong, On recurrences of Fahr and Ringel: an alternate approach, Fibonacci Quart. 48 (2010), no. 4, 363-365. H. Prodinger, Generating functions related to partition formulas for Fibonacci Numbers, JIS 11 (2008) 08.1.8. FORMULA G.f.: (3*sqrt(1-6*q+q^2)-(1+q))/(2*(1-7*q+q^2)) = 1 +2q +7q^2 +29q^3 +130q^4 + ... . Michael David Hirschhorn, Sep 03 2009 a(n) ~ 3*sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^(n+1) / (2*sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Sep 08 2014 Conjecture: n*a(n) + (-13*n+9)*a(n-1) + 22*(2*n-3)*a(n-2) + (-13*n+30)*a(n-3) + (n-3)*a(n-4) = 0. - R. J. Mathar, Aug 28 2015 EXAMPLE a(3) = 29 because 377 = 29 + 6*18 + 24*6 + 96*1. MAPLE a:= proc(n) option remember; `if`(n<4, [1, 2, 7, 29][n+1],        ((13*n-9)*a(n-1) -(44*n-66)*a(n-2)        +(13*n-30)*a(n-3) -(n-3)*a(n-4))/n)     end: seq(a(n), n=0..30);  # Alois P. Heinz, Jun 19 2013 MATHEMATICA a[n_] := a[n] = If[n<4, {1, 2, 7, 29}[[n+1]], ((13*n-9)*a[n-1] - (44*n-66)*a[n-2] + (13*n-30)*a[n-3] - (n-3)*a[n-4])/n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 07 2016, after Alois P. Heinz *) PROG (PARI) lista(nn) = my(q = qq + O(qq^nn)); gf = (3*sqrt(1-6*q+q^2) -(1+q))/(2*(1-7*q+q^2)); Vec(gf) \\ Michel Marcus, Jun 19 2013 CROSSREFS Cf. A110122. Sequence in context: A150664 A193040 A200755 * A007852 A300048 A232971 Adjacent sequences:  A132259 A132260 A132261 * A132263 A132264 A132265 KEYWORD nonn,easy AUTHOR Ph. Fahr and Claus Michael Ringel, Aug 19 2007 EXTENSIONS More terms from Michel Marcus, Jun 19 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 January 17 17:33 EST 2021. Contains 340247 sequences. (Running on oeis4.)