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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102592 a(n) = Sum_{k=0..n} binomial(2n+1, 2k)*5^(n-k). 1
 1, 8, 80, 832, 8704, 91136, 954368, 9994240, 104660992, 1096024064, 11477712896, 120196169728, 1258710630400, 13181388849152, 138037296103424, 1445545331654656, 15137947242201088, 158526641599938560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general, Sum_{k=0..n} binomial(2n+1,2k)*r^(n-k) has g.f. (1-(r-1)x)/(1-2(r+1)+(r-1)^2x^2) and a(n) = ((sqrt(r)-1)^(2n+1) + (sqrt(r)+1)^(2n+1))/(2*sqrt(r)). LINKS Index entries for linear recurrences with constant coefficients, signature (12,-16). FORMULA G.f.:(1-4x)/(1-12x+16x^2); a(n) = 12*a(n-1) - 16*a(n-2); a(n) = sqrt(5)*(sqrt(5)-1)^(2n+1)/10 + sqrt(5)*(sqrt(5)+1)^(2n+1)/10. a(n) = Sum_{k=0..n} binomial(2n+1, k+1)*5^k. - Paul Barry, May 27 2005 a(n) = 4^(n+1)*A001519(n+1). - N. J. A. Sloane, Apr 13 2011 CROSSREFS Cf. A066443, A102591. Sequence in context: A299871 A136949 A346178 * A345081 A320759 A233123 Adjacent sequences:  A102589 A102590 A102591 * A102593 A102594 A102595 KEYWORD easy,nonn AUTHOR Paul Barry, Jan 22 2005 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 July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)