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%I #76 Feb 09 2024 10:10:34
%S 1,3,6,8,11,13,16,18,21,23,26,28,31,33,36,38,41,43,46,48,51,53,56,58,
%T 61,63,66,68,71,73,76,78,81,83,86,88,91,93,96,98,101,103,106,108,111,
%U 113,116,118,121,123,126,128,131,133,136,138,141,143,146,148
%N Numbers that are congruent to {1, 3} mod 5.
%C A001844(N)= N^2 + (N+1)^2 is divisible by 5 if and only if N=a(n), n>=1. E.g., n=2: 5|(9 + 16), but 7^2 + 8^2 is not congruent 0 (mod 5). - _Wolfdieter Lang_, May 09 2012
%C The number of partitions of 5*(n-1) into at most 2 parts. - _Colin Barker_, Mar 31 2015
%H David Lovler, <a href="/A047219/b047219.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = floor((5*n-3)/2). - _Santi Spadaro_, Jul 24 2001, corrected by _Gary Detlefs_, Oct 28 2011
%F G.f.: x*(1 + 2*x + 2*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Oct 07 2011
%F a(n) = 2*n + floor((n-1)/2) - 1. - _Arkadiusz Wesolowski_, Sep 19 2012
%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1/2 + sqrt(5)/10)*Pi/5 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - _Amiram Eldar_, Dec 07 2021
%F E.g.f.: 2 + ((10*x - 7)*exp(x) - exp(-x))/4. - _David Lovler_, Aug 23 2022
%t Flatten[#+{1,3}&/@(5*Range[0,30])] (* _Harvey P. Dale_, Dec 22 2013 *)
%o (PARI) a(n)=(5*n-3)\2 \\ _Charles R Greathouse IV_, Oct 28 2011
%Y Cf. A000566, A001622, A212160, A212161.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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