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A073397
Eighth convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself.
3
1, 18, 198, 1680, 12060, 76824, 446952, 2420352, 12363120, 60151520, 280833696, 1265442048, 5528697408, 23507763840, 97575960960, 396398370816, 1579498956288, 6184543546368, 23833455191040, 90522348871680, 339263015528448, 1255995653197824, 4597442198728704
OFFSET
0,2
COMMENTS
For a(n) in terms of U(n+1) and U(n), with U(n) = A002605(n), see A073387 and the row polynomials of triangles A073405 and A073406.
LINKS
Index entries for linear recurrences with constant coefficients, signature (18,-126,384,-144,-2016,3360,4608,-12384,-8512, 24768,18432,-26880,-32256,4608,24576,16128,4608,512).
FORMULA
a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A002605(k) and c(k) = A073394(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+8, 8)*binomial(n-k, k)*2^(n-k).
G.f.: 1/(1-2*x*(1+x))^9.
MATHEMATICA
CoefficientList[Series[1/(1-2*x-2*x^2)^9, {x, 0, 30}], x] (* G. C. Greubel, Oct 06 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^9 )); // G. C. Greubel, Oct 06 2022
(SageMath)
def A073397_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-2*x-2*x^2)^9 ).list()
A073397_list(30) # G. C. Greubel, Oct 06 2022
CROSSREFS
Ninth (m=8) column of triangle A073387.
Sequence in context: A264356 A034727 A060532 * A020920 A083812 A086573
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved