OFFSET
1,1
COMMENTS
The sequence is infinite, since every number of the form 65*k + 56 is a member. - Arkadiusz Wesolowski, Oct 29 2013
REFERENCES
Wacław Sierpiński, 200 zadan z elementarnej teorii liczb, Warsaw: PZWS, 1964, pp. 5, 29.
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
W. Sierpiński, 250 Problems in Elementary Number Theory, (Modern Analytic and Computational Methods in Science and Mathematics, No. 26), American Elsevier Publishing Co., Inc., New York; PWN Polish Scientific Publishers, Warsaw, 1970, pp. 1, 23.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
From Bruno Berselli, Jan 12 2012: (Start)
G.f.: x*(4+5*x+47*x^2+5*x^3+4*x^4)/((1-x)^2*(1+x+x^2+x^3)).
a(n) = -a(-n+1) = (1/8)*(130*n+78*i^(n*(n+1))-45*(-1)^n-65), where i=sqrt(-1).
Sum(a(i), i=1..n) = a(A000982(n))+2*((-1)^n+1). (End)
MATHEMATICA
Select[Range[850], Divisible[4*#^2 + 1, 65] &]
Flatten[Table[65*k + n, {k, 0, 12}, {n, {4, 9, 56, 61}}]]
PROG
(PARI) for(n=4, 850, if((4*n^2+1)%65==0, print1(n, ", ")))
(PARI) forstep(n=4, 1e3, [5, 47, 5, 8], print1(n", ")) \\ Charles R Greathouse IV, Jan 13 2012
(Magma) m:=54; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(4+5*x+47*x^2+5*x^3+4*x^4)/((1-x)^2*(1+x+x^2+x^3)))); // Bruno Berselli, Jan 12 2012
(Maxima) makelist((1/8)*(130*n+78*%i^(n*(n+1))-45*(-1)^n-65), n, 1, 53); /* Bruno Berselli, Jan 12 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Arkadiusz Wesolowski, Jan 06 2012
STATUS
approved