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 A051920 a(n) = binomial(n, floor(n/2)) + 1. 9
 2, 2, 3, 4, 7, 11, 21, 36, 71, 127, 253, 463, 925, 1717, 3433, 6436, 12871, 24311, 48621, 92379, 184757, 352717, 705433, 1352079, 2704157, 5200301, 10400601, 20058301, 40116601, 77558761, 155117521, 300540196, 601080391, 1166803111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS With the exception of the initial 2s, these are numbers such that if Pascal's triangle is written in base a(n) - 1, the first n - 2 rows give the digits of the powers of a(n) written in that base. This is most often noticed for the powers of 11 since of course we use decimal. - Alonso del Arte, Jul 10 2011 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: -((2*x-1)*(3*x-1) +(x-1)*sqrt(1 - 4*x^2))/(2*x*(x-1)*(2*x-1)). - Thomas Baruchel, Jun 26 2018 0 = 1 +a(n)*(-2 +4*a(n+1) -2*a(n+2)) +a(n+1)*(-1 -2*a(n+1) +a(n+2)) +a(n+2) for all n>=0. - Michael Somos, Jun 30 2018 MAPLE a:= proc(n) option remember; `if`(n<3, [2, 2, 3][n+1],       ((n^2+n-4)*a(n-1) +2*(n-1)*(2*n-5)*a(n-2)        -4*(n-1)*(n-2)*a(n-3)) / ((n+1)*(n-2)))     end: seq(a(n), n=0..50);  # Alois P. Heinz, Mar 03 2014 MATHEMATICA a[n_] := a[n] = (4(n-1) a[n-2] + 2a[n-1] - 3n + 3)/(n+1); a[0] = a[1] = 2; Array[a, 50, 0] (* Jean-François Alcover, Jan 19 2017 *) Table[Binomial[n, Floor[n/2]], {n, 0, 40}]+1 (* Harvey P. Dale, Jan 20 2019 *) PROG (PARI) a(n)=binomial(n, n\2)+1 \\ Charles R Greathouse IV, Feb 05 2013 CROSSREFS Cf. A001405, A006481, A007318, A193242. Sequence in context: A243856 A173433 A053638 * A286350 A023105 A281723 Adjacent sequences:  A051917 A051918 A051919 * A051921 A051922 A051923 KEYWORD nonn AUTHOR N. J. A. Sloane, Dec 18 1999 STATUS approved

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Last modified October 16 13:29 EDT 2019. Contains 328091 sequences. (Running on oeis4.)