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

0,2

Comments

A131244 is a companion sequence.

Links

Table of n, a(n) for n=0..28.

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

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A371902 A267604 A099036 * A183314 A036886 A052251

Adjacent sequences: A131243 A131244 A131245 * A131247 A131248 A131249

Keyword

nonn

Author

Gary W. Adamson, Jun 22 2007

Status

approved