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A047355 Numbers that are congruent to {0, 3} mod 7. 13
0, 3, 7, 10, 14, 17, 21, 24, 28, 31, 35, 38, 42, 45, 49, 52, 56, 59, 63, 66, 70, 73, 77, 80, 84, 87, 91, 94, 98, 101, 105, 108, 112, 115, 119, 122, 126, 129, 133, 136, 140, 143, 147, 150, 154, 157, 161, 164, 168, 171, 175, 178, 182, 185, 189, 192, 196, 199, 203 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers k such that k^2/7 + k*(k + 1)/7 = k*(2*k + 1)/7 is a nonnegative integer. - Bruno Berselli, Feb 14 2017

LINKS

Table of n, a(n) for n=1..59.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

a(n) = a(n-2) + 7 = a(n-1) + a(n-2) - a(n-3). - Henry Bottomley, Jan 19 2001

a(n) = 7*n - a(n-1) - 11 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010

From Bruno Berselli, Sep 12 2011: (Start)

G.f.: x^2*(3 + 4*x)/((1 + x)*(1 - x)^2).

a(n) = (14*n - (-1)^n - 15)/4. (End)

a(n+1) = sum_{k>=0} {A030308(n,k)*A125176(k+2)}. - Philippe Deléham, Oct 17 2011.

a(n) = 2*n - 2 + floor((3*n - 3)/2). - Wesley Ivan Hurt, Jan 30 2014

MAPLE

A047355:=n->(14*n - (-1)^n - 15)/4; seq(A047355(n), n=1..100); # Wesley Ivan Hurt, Jan 30 2014

MATHEMATICA

Table[(14n - (-1)^n - 15)/4, {n, 100}] (* Wesley Ivan Hurt, Jan 30 2014 *)

PROG

(Haskell)

a047355 n = a047355_list !! (n-1)

a047355_list = scanl (+) 0 a010702_list -- Reinhard Zumkeller, Jul 05 2012

(PARI) a(n)=n\2*7 - 4 + n%2*4 \\ Charles R Greathouse IV, Aug 01 2016

CROSSREFS

Cf. A030123, A010702 (first differences).

Sequence in context: A288999 A310187 A198268 * A248522 A098005 A322533

Adjacent sequences:  A047352 A047353 A047354 * A047356 A047357 A047358

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 19 18:51 EDT 2019. Contains 326133 sequences. (Running on oeis4.)