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 A053311 Partial sums of A000285. 4
 1, 5, 10, 19, 33, 56, 93, 153, 250, 407, 661, 1072, 1737, 2813, 4554, 7371, 11929, 19304, 31237, 50545, 81786, 132335, 214125, 346464, 560593, 907061, 1467658, 2374723, 3842385, 6217112, 10059501, 16276617, 26336122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., pp. 189, 194-196. J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 224. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,0,-1). FORMULA a(n) = a(n-1) + a(n-2) + 4; a(0)=1, a(1)=5; n >= 1. a(n) = 4*F(n+2) + F(n+1) - 4, where F(k) is A000045(k). From R. J. Mathar, Apr 29 2013: (Start) G.f.: ( 1+3*x ) / ( (x-1)*(x^2+x-1) ). a(n) = A000071(n+3) + 3*A000071(n+2) = A000285(n+2) - 4. (End) MATHEMATICA CoefficientList[Series[(1+3*x)/((x-1)*(x^2+x-1)), {x, 0, 50}], x] (* G. C. Greubel, May 24 2018 *) PROG (PARI) x='x+O('x^30); Vec((1+3*x)/((x-1)*(x^2+x-1))) \\ G. C. Greubel, May 24 2018 (MAGMA) m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x)/((x-1)*(x^2+x-1)))); // G. C. Greubel, May 24 2018 CROSSREFS Cf. A000285. a(n) = A101220(4, 1, n+1). Sequence in context: A191595 A047882 A184260 * A147390 A300019 A115825 Adjacent sequences:  A053308 A053309 A053310 * A053312 A053313 A053314 KEYWORD easy,nonn AUTHOR Barry E. Williams, Mar 06 2000 STATUS approved

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Last modified January 17 06:34 EST 2019. Contains 319207 sequences. (Running on oeis4.)