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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
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
Sequence in context: A156156 A201486 A176617 * A358166 A372756 A195024
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 10 2015
STATUS
approved

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Last modified July 22 06:32 EDT 2024. Contains 374481 sequences. (Running on oeis4.)