OFFSET
1,3
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..500
P. A. Piza, Fermat coefficients, Math. Mag., 27 (1954), 141-146.
FORMULA
Following Piza's definition for the Fermat coefficients: (n:c)=binomial(2n-c, c-1)/c, a(n)= Round( sum_{c<=n & c odd} (n:c) ). - Pab Ter (pabrlos2(AT)yahoo.com), Oct 13 2005
EXAMPLE
n Sum_{c<=n & c odd} (n:c) a(n)
-------------------------------------
.1........1......................1
.2........1......................1
.3........2......................2
.4........4+1/3..................4
MAPLE
FermatCoeff:=(n, c)->binomial(2*n-c, c-1)/c:seq(round(add(FermatCoeff(n, 2*r+1), r=0..floor(n/2))), n=1..40); # Pab Ter, Oct 13 2005
MATHEMATICA
F[n_, c_]:=Binomial[2n - c, c - 1]/c; Table[Round[Sum[F[n, 2r + 1], {r, 0, Floor[n/2]}]], {n, 40}] (* Indranil Ghosh, Apr 01 2017 *)
PROG
(PARI) F(n, c) = binomial(2*n - c, c - 1)/c;
for(n=1, 40, print1(round(sum(r=0, floor(n/2), F(n, 2*r + 1))), ", ")) \\ Indranil Ghosh, Apr 01 2017
(Python)
from sympy import binomial
def F(n, c): return binomial(2*n - c, c - 1)/c
print([int(round(sum([F(n, 2*r + 1) for r in range(n//2 + 1)]))) for n in range(1, 41)]) # Indranil Ghosh, Apr 01 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 13 2005
STATUS
approved