0,2

a(n-1)=sum(P(5;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=4. These are the sums of the SW-NE diagonals in P(5;n,k), the (5,1) Pascal triangle A093562. Observation by Paul Barry (pbarry(AT)wit.ie, Apr 29 2004. Proof via recursion relations and comparison of inputs. Also sums of the SW-NE diagonals in the (1,4)-Pascal triangle A095666.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=5. a(-1):=4.

G.f.: (1+4*x)/(1-x-x^2).

Row sums of triangle A131776 starting (1, 5, 6, 11, 17, 28,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 14 2007

a(n)=4*fibonacci(n-1)+fibonacci(n), n>=1 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 05 2007

a(n)=((1+sqrt5)^n-(1-sqrt5)^n)/(2^n*sqrt5)+ 2*((1+sqrt5)^(n-1)-(1-sqrt5)^(n-1))/(2^(n-2)*sqrt5). Offset 1. a(3)=6 [From Al Hakanson (hawkuu(AT)gmail.com), Jan 14 2009]

a:=n->4*fibonacci(n-1)+fibonacci(n): seq(a(n), n=1..32); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 05 2007

a={}; b=1; c=5; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 9, 1}]; a (Vladimir Orlovsky, Jul 22 2008)

a(n) = A101220(4, 0, n+1).

a(n) = A109754(4, n+1).

Cf. A131776.

Sequence in context: A136974 A101187 A070373 this_sequence A042531 A042839 A041373

Adjacent sequences: A022092 A022093 A022094 this_sequence A022096 A022097 A022098

nonn

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