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A000967 Sum of Fermat coefficients.
(Formerly M1148 N0437)
3
1, 2, 4, 8, 18, 40, 91, 210, 492, 1165, 2786, 6710, 16267, 39650, 97108, 238824, 589521, 1459960, 3626213, 9030450, 22542396, 56393792, 141358274, 354975429, 892893120, 2249412290, 5674891000, 14335757256, 36259245522, 91815545800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

R. P. Loh, A. G. Shannon, A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980.

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=1..n} (n:c) ). - Pab Ter (pabrlos2(AT)yahoo.com), Oct 13 2005

a(n) = rounded(sum(A258993(n,k)/(2*k+1)): k = 0..n-1). - Reinhard Zumkeller, Jun 22 2015

EXAMPLE

n...Sum_{c=1..n} (n:c).....a(n)

--------------------------------

.1........1.................1

.2........2.................2

.3........4.................4

.4........8+1/3.............8

MAPLE

FermatCoeff:=(n, c)->binomial(2*n-c, c-1)/c:seq(round(add(FermatCoeff(n, c), c=1..n)), n=1..40); # Pab Ter, Oct 13 2005

PROG

(Haskell)

import Data.Function (on)

a000967 n = round $ sum $

            zipWith ((/) `on` fromIntegral) (a258993_row n) [1, 3 ..]

-- Reinhard Zumkeller, Jun 22 2015

CROSSREFS

Cf. A143858, A258708.

Sequence in context: A056362 A086585 A052910 * A288309 A096813 A058387

Adjacent sequences:  A000964 A000965 A000966 * A000968 A000969 A000970

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 13 2005

STATUS

approved

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Last modified November 13 02:28 EST 2018. Contains 317120 sequences. (Running on oeis4.)