A045809 9-ish numbers (end in 13, 37, 59, 91).
13, 37, 59, 91, 113, 137, 159, 191, 213, 237, 259, 291, 313, 337, 359, 391, 413, 437, 459, 491, 513, 537, 559, 591, 613, 637, 659, 691, 713, 737, 759, 791, 813, 837, 859, 891, 913, 937, 959, 991, 1013, 1037, 1059, 1091, 1113, 1137, 1159, 1191, 1213, 1237
Offset: 1
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
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Haskell
import Data.List (findIndices) a045809 n = a045809_list !! (n-1) a045809_list = findIndices (`elem` [13,37,59,91]) $ cycle [0..99] -- Reinhard Zumkeller, Jan 23 2012
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Mathematica
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 *) LinearRecurrence[{1,0,0,1,-1},{13,37,59,91,113},50] (* Harvey P. Dale, Feb 03 2024 *)
Formula
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
a(n) = (50*n+4*i^(n*(n-1))+3*(-1)^n-25)/2, where i=sqrt(-1). - Bruno Berselli, Feb 22 2012
Extensions
More terms from Erich Friedman.