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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

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-Fran├žois Alcover, Jan 19 2017 *)

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 February 19 03:37 EST 2018. Contains 299330 sequences. (Running on oeis4.)