A105871 - OEIS

A105871

a(n) = sum{k=0..floor(n/2), C(2*n-3*k, n)*C(n-k, k)}

1, 2, 6, 22, 85, 336, 1350, 5492, 22554, 93300, 388201, 1622868, 6811056, 28680356, 121111440, 512684484, 2174928031, 9243973062, 39354962345, 167799259130, 716414975613, 3062437147352, 13105366936465, 56139506687280

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(n) = sum{k=0..floor(n/2), C(2*n-3*k, n)*C(n-k, k)}

Conjecture: 5*n*(n-1)*(3*n-10)*a(n) -3*(n-1)*(21*n^2-63*n-20)*a(n-1) +3*(-3*n^3+107*n^2-446*n+444)*a(n-2) +(3*n^3-259*n^2+1279*n-1575)*a(n-3) +3*(-21*n^3+210*n^2-673*n+694)*a(n-4) -3*(n-3)*(3*n^2-8*n-7)*a(n-5) -2*(n-4)*(3*n-7)*(2*n-9)*a(n-6)=0. - R. J. Mathar, Feb 20 2015

MAPLE

A105871 := proc(n)

add(binomial(2*n-3*k, n)*binomial(n-k, k), k=0..floor(n/2)) ;

end proc: # R. J. Mathar, Feb 20 2015

MATHEMATICA

Table[Sum[Binomial[2n-3k, n]Binomial[n-k, k], {k, 0, Floor[n/2]}], {n, 0, 30}] (* Harvey P. Dale, Jan 23 2023 *)

PROG

(PARI) a(n)=sum(k=0, floor(n/2), binomial(2*n-3*k, n)*binomial(n-k, k) ); /* Joerg Arndt, Mar 06 2013 */

CROSSREFS

Sequence in context: A279563 A150247 A150248 * A150249 A150250 A150251

Adjacent sequences: A105868 A105869 A105870 * A105872 A105873 A105874

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 23 2005

STATUS

approved