A131246 Row sums of triangle A131245.

1, 3, 6, 13, 27, 57, 119, 250, 523, 1097, 2297, 4815, 10086, 21137, 44283, 92793, 194419, 407378, 853559, 1788481, 3747361, 7851867, 16451910, 34471669, 72228171, 151339401, 317100335, 664418698, 1392152131

Offset: 0

Author

Gary W. Adamson, Jun 22 2007

Keywords

• nonn

Comments

A131244 is a companion sequence.

Examples

			a(3) = 13 = sum of row 3 terms of triangle A131245: (5 + 5 + 2 + 1)
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-1)

Crossrefs

Cf. A131243, A131244, A131245, A065941, A046854.

Programs

Maple

A046854 := proc(n,k) binomial(floor((n+k)/2),k) ; end proc:
A131245 := proc(n,k) local a,j ; a := 0 ; for j from k to n do a := a+ A046854(n,j)*A046854(j,k) ;  end do: a ; end proc:
A131246 := proc(n) add(A131245(n,k),k=0..n) ; end proc:
seq(A131246(n),n=0..50) ; # R. J. Mathar, Jan 29 2011

Mathematica

CoefficientList[Series[-(1+x)(x^2-x-1)/(1-x-3x^2+x^3+x^4),{x,0,30}],x] (* or *) LinearRecurrence[{1,3,-1,-1},{1,3,6,13},30] (* Harvey P. Dale, Sep 07 2013 *)

Formula

G.f. -(1+x)*(x^2-x-1)/ ( 1-x-3*x^2+x^3+x^4 ). - R. J. Mathar, Jan 29 2011

a(0)=1, a(1)=3, a(2)=6, a(3)=13, a(n)=a(n-1)+3*a(n-2)-a(n-3)-a(n-4). - Harvey P. Dale, Sep 07 2013