A045809 - OEIS

%I #27 Feb 03 2024 13:01:52

%S 13,37,59,91,113,137,159,191,213,237,259,291,313,337,359,391,413,437,

%T 459,491,513,537,559,591,613,637,659,691,713,737,759,791,813,837,859,

%U 891,913,937,959,991,1013,1037,1059,1091,1113,1137,1159,1191,1213,1237

%N 9-ish numbers (end in 13, 37, 59, 91).

%H Reinhard Zumkeller, <a href="/A045809/b045809.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F G.f.: x*(13+24*x+22*x^2+32*x^3+9*x^4)/(1-x-x^4+x^5). - _Colin Barker_, Jan 23 2012

%F a(n) = (50*n+4*i^(n*(n-1))+3*(-1)^n-25)/2, where i=sqrt(-1). - _Bruno Berselli_, Feb 22 2012

%t CoefficientList[Series[(13 + 24*x + 22*x^2 + 32*x^3 + 9*x^4)/(1 - x - x^4 + x^5), {x, 0, 80}], x] (* _Wesley Ivan Hurt_, Jan 23 2017 *)

%t LinearRecurrence[{1,0,0,1,-1},{13,37,59,91,113},50] (* _Harvey P. Dale_, Feb 03 2024 *)

%o (Haskell)

%o import Data.List (findIndices)

%o a045809 n = a045809_list !! (n-1)

%o a045809_list = findIndices (`elem` [13,37,59,91]) $ cycle [0..99]

%o -- _Reinhard Zumkeller_, Jan 23 2012

%Y Cf. A045800-A045808, A045572, A045797, A045798.

%K nonn,base,easy

%O 1,1

%A _J. H. Conway_

%E More terms from _Erich Friedman_.