The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A054452 Partial sums of A027941(n-1) with a(-1) = 0. 7
 0, 0, 1, 5, 17, 50, 138, 370, 979, 2575, 6755, 17700, 46356, 121380, 317797, 832025, 2178293, 5702870, 14930334, 39088150, 102334135, 267914275, 701408711, 1836311880, 4807526952, 12586269000, 32951280073, 86267571245, 225851433689, 591286729850 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 László Németh, Pascal pyramid in the space H^2 x R, arXiv:1701.06022 [math.CO], 2017 (5th line of Table 1 is a(n-2)). A. Shriki and O. Liba, Polygons with Fibonacci Number Coordinates: Problem B-1167, Fib. Quart. 54,2 May 2016, p. 180-181. Index entries for linear recurrences with constant coefficients, signature (5,-8,5,-1). FORMULA a(n) = +5*a(n-1) -8*a(n-2) +5*a(n-3) -1*a(n-4). G.f.: x^2/((1-x)^2*(1-3*x+x^2)). a(n) = Sum_{k=0..n} A027941(k-1) = F(2*n)-n = A054450(2*n-1, 2) = A054451(2*n-3). G.f.: x^2*Fibe(x)/(1-x)^2, with Fibe(x) := 1/(1-3*x+x^2) = g.f. A001906(n+1) (Fibonacci numbers F(2(n+1))). Fourth diagonal of array defined by T(i, 1) = T(1, j) = 1, T(i, j) = Max(T(i-1, j) + T(i-1, j-1); T(i-1, j-1) + T(i, j-1)). - Benoit Cloitre, Aug 05 2003 a(n) = Sum_{k=0..n-2} binomial(2*n-k-1, k). - Johannes W. Meijer, Aug 12 2013 a(n) = Sum_{i=1..n-1} Sum_{j=1..n-1} binomial(i+j, i-j). - Wesley Ivan Hurt, Mar 25 2015 a(n) = Sum_{k=0..n} (binomial(n+1,k+2)*Fibonacci(k)). - Vladimir Kruchinin, Oct 21 2016 a(n) = (-((3-sqrt(5))/2)^n + ((3+sqrt(5))/2)^n)/sqrt(5) - n. - Colin Barker, Jan 28 2017 MAPLE a[0]:=0: a[1]:=1: for n from 2 to 50 do a[n] := 3*a[n-1]-a[n-2] od: seq(a[n]-n, n=0..27); # Zerinvary Lajos, Mar 20 2008 with(combinat): seq(fibonacci(2*n)-n, n=0..27); # Zerinvary Lajos, Jun 19 2008 g:=z/(1-3*z+z^2): gser:=series(g, z=0, 43): seq(abs(coeff(gser, z, n)-n), n=0..27); # Zerinvary Lajos, Mar 22 2009 MATHEMATICA CoefficientList[Series[x^2 / ((1 - x)^2 (1 - 3 x + x^2)), {x, 0, 33}], x] (* Vincenzo Librandi, Mar 26 2015 *) PROG (Sage) [(lucas_number1(n, 3, 1)-lucas_number1(n, 2, 1)) for n in range(1, 28)]# Zerinvary Lajos, Mar 13 2009 (Magma) I:=[0, 0, 1, 5]; [n le 4 select I[n] else 5*Self(n-1)-8*Self(n-2)+5*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Mar 26 2015 (Maxima) makelist(sum(fib(k)*binomial(n+1, k+2), k, 0, n), n, 0, 20); /* Vladimir Kruchinin, Oct 21 2016 */ (PARI) concat(vector(2), Vec(x^2/((1-x)^2*(1-3*x+x^2)) + O(x^40))) \\ Colin Barker, Jan 28 2017 CROSSREFS Cf. A027941, A054451, A001906, A052952. Sequence in context: A273688 A146045 A086866 * A196310 A196283 A196333 Adjacent sequences: A054449 A054450 A054451 * A054453 A054454 A054455 KEYWORD easy,nonn AUTHOR Wolfdieter Lang, Apr 27 2000 EXTENSIONS More terms from James A. Sellers, Apr 28 2000 a(0) added by Arkadiusz Wesolowski, Jun 07 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 12 03:53 EDT 2024. Contains 375085 sequences. (Running on oeis4.)