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 A027947 a(n) = Sum_{k=m..n} T(k,n-k), where m = floor((n+1)/2); a(n) is the n-th diagonal-sum of left justified array T given by A027935. 1
 1, 1, 2, 3, 4, 7, 9, 15, 21, 32, 48, 70, 107, 156, 236, 349, 521, 778, 1155, 1728, 2567, 3833, 5707, 8505, 12680, 18884, 28158, 41943, 62520, 93160, 138825, 206897, 308290, 459459, 684652, 1020311, 1520473, 2265815, 3376605 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1). FORMULA G.f.: (1 + x)/(1 - 2*x^2 - x^3 + x^4). MAPLE seq(coeff(series((1+x)/(1-2*x^2-x^3+x^4), x, n+1), x, n), n = 0..40); # G. C. Greubel, Sep 29 2019 MATHEMATICA LinearRecurrence[{0, 2, 1, -1}, {1, 1, 2, 3}, 40] (* G. C. Greubel, Sep 29 2019 *) PROG (PARI) my(x='x+O('x^40)); Vec((1+x)/(1-2*x^2-x^3+x^4)) \\ G. C. Greubel, Sep 29 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)/(1-2*x^2-x^3+x^4) )); // G. C. Greubel, Sep 29 2019 (Sage) def A027947_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P((1+x)/(1-2*x^2-x^3+x^4)).list() A027947_list(40) # G. C. Greubel, Sep 29 2019 (GAP) a:=[1, 1, 2, 3];; for n in [5..40] do a[n]:=2*a[n-2]+a[n-3]-a[n-4]; od; a; # G. C. Greubel, Sep 29 2019 CROSSREFS Cf. A027935. Sequence in context: A108809 A276846 A303665 * A324736 A293853 A067236 Adjacent sequences:  A027944 A027945 A027946 * A027948 A027949 A027950 KEYWORD nonn AUTHOR STATUS approved

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Last modified August 3 10:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)