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A131246 Row sums of triangle A131245. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A094386 A267604 A099036 * A183314 A036886 A052251

Adjacent sequences:  A131243 A131244 A131245 * A131247 A131248 A131249

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jun 22 2007

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)