A047374 - OEIS

%I #54 Nov 04 2022 20:14:16

%S 4,5,11,12,18,19,25,26,32,33,39,40,46,47,53,54,60,61,67,68,74,75,81,

%T 82,88,89,95,96,102,103,109,110,116,117,123,124,130,131,137,138,144,

%U 145,151,152,158,159,165,166,172

%N Numbers that are congruent to {4, 5} mod 7.

%H Daniel Starodubtsev, <a href="/A047374/b047374.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F G.f.: x*(4 + x + 2*x^2)/((1 + x)*(x - 1)^2). - _R. J. Mathar_, Dec 04 2011

%F a(n) = -(5/4)*(-1)^n + 7*(n-1)/2 + 11/4. - _Viet Quoc Le Tran_, Jun 14 2014

%F a(n) = (14*n - 5*(-1)^n - 3)/4. - _David Lovler_, Sep 15 2022

%F E.g.f.: 2 + ((14*x - 3)*exp(x) - 5*exp(-x))/4. - _David Lovler_, Sep 15 2022

%t Select[Range[200], MemberQ[{4, 5}, Mod[#, 7]] &] (* _Amiram Eldar_, May 07 2021 *)

%o (PARI) a(n) = (14*n - 5*(-1)^n - 3)/4 \\ _David Lovler_, Sep 15 2022

%Y Cf. A017029, A017041.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_