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 A054455 Row sums of triangle A054453. 3
 1, 3, 7, 16, 34, 70, 140, 274, 527, 999, 1871, 3468, 6371, 11613, 21023, 37826, 67688, 120530, 213670, 377252, 663607, 1163361, 2033101, 3542808, 6157045, 10673703, 18460759, 31859716, 54872158, 94326622 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,0,-5,0,3,1). FORMULA a(n) = Sum_{m=0..n} A054453(n, m). a(n) = ((5*n^2 + 27*n + 50)*F(n+1) + 34*(n+1)*F(n))/50, F(n)= A000045(n) (Fibonacci numbers). G.f.: ((Fib(x))^3)*(1-x^2)^2, with Fib(x)=1/(1-x-x^2) g.f. for A000045(n+1) (Fibonacci numbers without F(0)). MATHEMATICA LinearRecurrence[{3, 0, -5, 0, 3, 1}, {1, 3, 7, 16, 34, 70}, 40] (* or *) CoefficientList[Series[(1-x^2)^2/(1-x-x^2)^3, {x, 0, 40}], x] (* G. C. Greubel, Jan 31 2019 *) PROG (PARI) my(x='x+O('x^30)); Vec((1-x^2)^2/(1-x-x^2)^3) \\ G. C. Greubel, Jan 31 2019 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1-x^2)^2/(1-x-x^2)^3 )); // G. C. Greubel, Jan 31 2019 (Sage) ((1-x^2)^2/(1-x-x^2)^3).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019 (GAP) a:=[1, 3, 7, 16, 34, 70];; for n in [7..30] do a[n]:=3*a[n-1]-5*a[n-3] +3*a[n-5]+a[n-6]; od; a; # G. C. Greubel, Jan 31 2019 CROSSREFS Cf. A054453, A000045. Sequence in context: A014668 A182615 A181893 * A178455 A281811 A238089 Adjacent sequences:  A054452 A054453 A054454 * A054456 A054457 A054458 KEYWORD easy,nonn AUTHOR Wolfdieter Lang, Apr 27 2000 STATUS approved

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Last modified October 22 18:31 EDT 2019. Contains 328319 sequences. (Running on oeis4.)