A134720 -id:A134720 - cp's OEIS frontend

A047350 Numbers that are congruent to {1, 2, 4} mod 7.

1, 2, 4, 8, 9, 11, 15, 16, 18, 22, 23, 25, 29, 30, 32, 36, 37, 39, 43, 44, 46, 50, 51, 53, 57, 58, 60, 64, 65, 67, 71, 72, 74, 78, 79, 81, 85, 86, 88, 92, 93, 95, 99, 100, 102, 106, 107, 109, 113, 114, 116, 120, 121, 123, 127, 128, 130, 134, 135, 137, 141

Offset: 1

N. J. A. Sloane

a(n+1) = a(n) + (a(n) mod 7). - Ben Paul Thurston, Jan 09 2008
Also defined by: a(1)=1, and a(n) = smallest number larger than a(n-1) such that a(n)^3 - a(n-1)^3 is divisible by 7. - Zak Seidov, Apr 21 2009
Union of A047353 and A017029. - R. J. Mathar, Apr 28 2009
Indices of the even numbers in the Padovan sequence. - Francesco Daddi, Jul 31 2011
Euler's problem (see Link lines, English translation by David Zao): Finding the values of a so that the form a^3-1 is divisible by 7. The three residuals that remain after the division of any square by 7 are 1, 2 and 4. Hence the values are 7n+1, 7n+2, 7n+4. - Bruno Berselli, Oct 24 2012

Leonhard Euler, The Euler Archive, Theoremata circa divisores numerorum (E134), Novi Commentarii academiae scientiarum imperialis Petropolitanae, Volume 1 (1750), p. 40 (Theorem II, example 2).
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A000931, A017029, A047353, A134720.

[n : n in [0..150] | n mod 7 in [1, 2, 4]]; // Wesley Ivan Hurt, Jun 13 2016

A047350:=n->(21*n-21-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047350(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016

Select[Range[0, 150], MemberQ[{1, 2, 4}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Jun 13 2016 *)

a(n)=n\3*7+[-3,1,2][n%3+1] \\ Charles R Greathouse IV, Jul 31 2011

From R. J. Mathar, Apr 28 2009: (Start)
G.f.: x*(1 + x + 2*x^2 + 3*x^3)/((1 + x + x^2)*(x-1)^2).
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.
a(n) = a(n-3) + 7 for n > 3. (End)
From Wesley Ivan Hurt, Jun 13 2016: (Start)
a(n) = (21*n - 21 - 6*cos(2*n*Pi/3) + 4*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 7k-3, a(3k-1) = 7k-5, a(3k-2) = 7k-6. (End)
a(n) = 4*n - 3 - 2*floor(n/3) - 3*floor((n+1)/3). - Ridouane Oudra, Nov 23 2022

A135619 Even Padovan numbers divided by 2.

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 6, 8, 14, 43, 57, 100, 308, 408, 716, 2205, 2921, 5126, 15786, 20912, 36698, 113015, 149713, 262728, 809096, 1071824, 1880920, 5792473, 7673393, 13465866, 41469422, 54935288, 96404710, 296887523, 393292233, 690179756, 2125474556, 2815654312

Offset: 1

Omar E. Pol, Feb 17 2008

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 7, 0, 0, 1, 0, 0, 1).

Cf. A000931, A134720.

#/2&/@Select[Join[{0,0,0},LinearRecurrence[{0,1,1},{1,1,1}, 100]], EvenQ] (* Harvey P. Dale, May 11 2011 *)
LinearRecurrence[{0, 0, 7, 0, 0, 1, 0, 0, 1},{0, 0, 0, 1, 1, 2, 6, 8, 14}, 40] (* Ray Chandler, Mar 03 2024 *)

a(n) = A134720(n)/2.

G.f.: -x^4*(x^4-x^3+2*x^2+x+1) / (x^9+x^6+7*x^3-1). - Colin Barker, Sep 18 2013

More terms from Harvey P. Dale, May 11 2011

cp's OEIS Frontend

A047350 Numbers that are congruent to {1, 2, 4} mod 7.

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