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A073378
Eighth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.
3
1, 9, 63, 345, 1665, 7227, 29073, 109791, 394020, 1354210, 4486482, 14397318, 44932446, 136817370, 407566350, 1190446866, 3415935699, 9645169743, 26836557825, 73670997015, 199751003991, 535449185469
OFFSET
0,2
COMMENTS
For a(n) in terms of U(n+1) and U(n) with U(n) = A001045(n+1) see A073370 and the row polynomials of triangles A073399 and A073400.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-18,-60,234,126,-1176,36,3519,-479,-7038,144, 9408,2016,-7488,-3840,2304,2304,512).
FORMULA
a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073377(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+8, 8) * binomial(n-k, k) * 2^k.
G.f.: 1/(1-(1+2*x)*x)^9 = 1/((1+x)*(1-2*x))^9.
MATHEMATICA
CoefficientList[Series[1/((1+x)*(1-2*x))^9, {x, 0, 40}], x] (* G. C. Greubel, Oct 01 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^9 )); // G. C. Greubel, Oct 01 2022
(SageMath)
def A073378_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1+x)*(1-2*x))^9 ).list()
A073378_list(40) # G. C. Greubel, Oct 01 2022
CROSSREFS
Ninth (m=8) column of triangle A073370.
Sequence in context: A178161 A015669 A202982 * A316461 A022733 A111997
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved