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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

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

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Last modified August 16 05:55 EDT 2022. Contains 356160 sequences. (Running on oeis4.)