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A108475 Expansion of (1-3*x) / (1-5*x-5*x^2+x^3). 4
1, 2, 15, 84, 493, 2870, 16731, 97512, 568345, 3312554, 19306983, 112529340, 655869061, 3822685022, 22280241075, 129858761424, 756872327473, 4411375203410, 25711378892991, 149856898154532, 873430010034205, 5090723162050694, 29670908962269963 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of A108477. In general, sum{k=0..n, sum{j=0..n, C(2(n-k),j)C(2k,j)r^j}} has expansion (1-(r+1)x)/((1+(r+3)x+(r-1)(r+3)x^2+(r-1)^3*x^3).

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,5,-1).

FORMULA

G.f.: (1-3*x)/((1+x)*(1-6*x+x^2)).

a(n) = 5*a(n-1)+5*a(n-2)-a(n-3).

a(n) = sum{k=0..n, sum{j=0..n, C(2(n-k), j)C(2*k, j)2^j}}.

Conjecture: a(n)=A000129(n+1)*A001333(n). - R. J. Mathar, Jul 08 2009

a(n)+a(n+1) = A001541(n+1). - R. J. Mathar, Jul 13 2009

a(n) = (4*(-1)^n-(3-2*sqrt(2))^n*(-2+sqrt(2))+(2+sqrt(2))*(3+2*sqrt(2))^n)/8. - Colin Barker, Nov 04 2016

PROG

(PARI) Vec((1-3*x)/((1+x)*(1-6*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 04 2016

CROSSREFS

Sequence in context: A057152 A002740 A178750 * A098624 A116079 A153445

Adjacent sequences:  A108472 A108473 A108474 * A108476 A108477 A108478

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 04 2005

STATUS

approved

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Last modified November 18 19:06 EST 2017. Contains 294894 sequences.