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A052960 Expansion of ( 1-x-x^2 ) / ( 1-2*x-2*x^2+x^3+x^4 ). 3
1, 1, 3, 7, 18, 46, 118, 303, 778, 1998, 5131, 13177, 33840, 86905, 223182, 573157, 1471933, 3780093, 9707713, 24930522, 64024444, 164422126, 422254905, 1084399096, 2784861432, 7151844025, 18366756913, 47167941348, 121132691065 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Diagonal sums of the Riordan matrix ((1-x-x^2)/(1-2x-x^2),(x-x^2-x^3)/(1-2x-x^2)) (A190215) [Emanuele Munarini, May 10 2011]

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1031

Index entries for linear recurrences with constant coefficients, signature (2,2,-1,-1)

FORMULA

G.f.: (1-x-x^2)/(1-2*x-2*x^2+x^3+x^4)

Recurrence: {a(1)=1, a(0)=1, a(2)=3, a(3)=7, a(n)+a(n+1)-2*a(n+2)-2*a(n+3)+a(n+4)=0}

Sum(-1/331*(-25-75*_alpha+6*_alpha^2+5*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-2*_Z^2+_Z^3+_Z^4))

a(n) = sum(sum(binomial(i+2*k,2*k)*binomial(i+k,n-i-2*k),k=0..n/2),i=0..n) [Emanuele Munarini, May 10 2011]

MAPLE

spec := [S, {S=Sequence(Prod(Union(Sequence(Union(Prod(Z, Z), Z)), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);

MATHEMATICA

Table[Sum[Sum[Binomial[i+2k, 2k]Binomial[i+k, n-i-2k], {k, 0, n/2}], {i, 0, n}], {n, 0, 12}] [Emanuele Munarini, May 10 2011]

PROG

(Maxima) makelist(sum(sum(binomial(i+2*k, 2*k)*binomial(i+k, n-i-2*k), k, 0, n/2), i, 0, n), n, 0, 24); [Emanuele Munarini, May 10 2011]

CROSSREFS

Sequence in context: A114713 A078058 A116413 * A059512 A094297 A026107

Adjacent sequences:  A052957 A052958 A052959 * A052961 A052962 A052963

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

EXTENSIONS

More terms from James A. Sellers, Feb 06 2000

STATUS

approved

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Last modified April 26 12:00 EDT 2019. Contains 322472 sequences. (Running on oeis4.)