0,3

Inverse binomial transform of powers of 5 (A000351) preceded by 0. - Paul Barry (pbarry(AT)wit.ie), Apr 02 2003

Number of walks of length n between any two distinct vertices of the complete graph K_5. Example: a(2)=3 because the walks of length 2 between the vertices A and B of the complete graph ABCDE are: ACB, ADB, AEB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004

The terms of the sequence are the number of segments (sides) per iteration of the space-filling Peano-Hilbert curve. - Giorgio Balzarotti (greenblue(AT)tiscali.it), Mar 16 2006

a(n)=4^n/5-(-1)^n/5. E.g.f. (exp(4x)-exp(-x))/5. - Paul Barry (pbarry(AT)wit.ie), Apr 02 2003

a(n)=sum{k=1..n, binomial(n, k)(-1)^(n+k)*5^(k-1) }. - Paul Barry (pbarry(AT)wit.ie), May 13 2003

a(2n) = 4*a(2n-1) -1, a(2n+1) = 4*a(2n) +1. In general this is true for all sequences of the type a(n) +a(n+1) = q^(n): i.e. a(2n) = q*a(2n-1) -1 and a(2n+1) = q*a(2n) +1. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 15 2003

a(n)=4^(n-1) - a(n-1). G.f.=x/(1-3x-4x^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004

a(n+1)=sum{k=0..floor(n/2), binomial(n-k, k)3^(n-2k)4^k} - Paul Barry (pbarry(AT)wit.ie), Jul 29 2004

a(n)=4a(n-1)-(-1)^n, n>0, a(0)=0. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2004

a(-1)=0 sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(1, 3, 3, 4, lambda n: 0) sage: [it.next() for i in xrange(0, 24)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008

Cf. A015518, A001045.

Sequence in context: A101052 A016064 A014985 this_sequence A098619 A086608 A037772

Adjacent sequences: A015518 A015519 A015520 this_sequence A015522 A015523 A015524

nonn,easy

Olivier Gerard (ogerard(AT)ext.jussieu.fr)