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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
FORMULA
a(n) = a(n-2) + 7 = a(n-1) + a(n-2) - a(n-3). - Henry Bottomley, Jan 19 2001
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
E.g.f.: 4 + ((14*x - 15)*exp(x) - exp(-x))/4. - David Lovler, Aug 31 2022
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified July 12 16:16 EDT 2024. Contains 374251 sequences. (Running on oeis4.)