0,2

Second binomial transform of (1,1,5,5,25,25,....). - Paul Barry (pbarry(AT)wit.ie), Jul 16 2003

a(n) = A167808(3*n+1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 12 2009]

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

a(n) = 4a(n-1)+a(n-2), n>1, a(0)=1, a(1)=3; G.f.: (1-x)/(1-4*x-x^2); a(n)=[ (1+sqrt(5))(2+sqrt(5))^n - (1-sqrt(5))(2-sqrt(5))^n ]/2*sqrt(5).

a(n)=sum{k=0..n, sum{j=0..n-k, C(n,j)C(n-j,k)F(n-j+1)}}; - Paul Barry (pbarry(AT)wit.ie), May 19 2006

a(n)=second binomial transform of 1,1,5,5,25,25,125,125. This is 5^n offset 0 doubled. Also it is 1 + the first differencing of((2+sqrt5)^n-(2-sqrt5)^n)/sqrt20 offset 1. [From Al Hakanson (hawkuu(AT)gmail.com), May 02 2009]

with(combinat): a:=n->fibonacci(n, 4)-fibonacci(n-1, 4): seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008

A033887(n)=A001076(n)+A001077(n).

Equals 2*A049651(n) + 1.

Sequence in context: A140320 A037583 A093834 this_sequence A117376 A151318 A151212

Adjacent sequences: A033884 A033885 A033886 this_sequence A033888 A033889 A033890

nonn,easy,new

N. J. A. Sloane (njas(AT)research.att.com).