|
| |
|
|
A254895
|
|
Indices of octagonal numbers (A000567) that are also centered square numbers (A001844).
|
|
3
|
|
|
|
1, 13, 53, 1241, 5161, 121573, 505693, 11912881, 49552721, 1167340733, 4855660933, 114387478921, 475805218681, 11208805593493, 46624055769773, 1098348560683361, 4568681660219041, 107626950141375853, 447684178645696213, 10546342765294150201
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Also positive integers x in the solutions to 6*x^2 - 4*y^2 - 4*x + 4*y - 2 = 0, the corresponding values of y being A253673.
|
|
|
LINKS
|
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).
|
|
|
FORMULA
|
a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+12*x^3-58*x^2+12*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).
|
|
|
EXAMPLE
|
13 is in the sequence because the 13th octagonal number is 481, which is also the 16th centered square number.
|
|
|
PROG
|
(PARI) Vec(-x*(x^4+12*x^3-58*x^2+12*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))
|
|
|
CROSSREFS
|
Cf. A000567, A001844, A253673, A254896.
Sequence in context: A156156 A201486 A176617 * A195024 A071230 A027000
Adjacent sequences: A254892 A254893 A254894 * A254896 A254897 A254898
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Colin Barker, Feb 10 2015
|
|
|
STATUS
|
approved
|
| |
|
|
