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A253674 Indices of centered octagonal numbers (A016754) which are also centered triangular numbers (A005448). 3
1, 10, 40, 931, 3871, 91180, 379270, 8934661, 37164541, 875505550, 3641745700, 85790609191, 356853914011, 8406604195120, 34968041827330, 823761420512521, 3426511245164281, 80720212606031890, 335763133984272160, 7909757073970612651, 32901360619213507351 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers y in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of x 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^2-5*x+1)*(x^2+14*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

EXAMPLE

10 is in the sequence because the 10th centered octagonal number is 361, which is also the 16th centered triangular number.

MATHEMATICA

LinearRecurrence[{1, 98, -98, -1, 1}, {1, 10, 40, 931, 3871}, 30] (* Harvey P. Dale, Oct 01 2015 *)

PROG

(PARI) Vec(-x*(x^2-5*x+1)*(x^2+14*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

CROSSREFS

Cf. A005448, A016754, A253673, A253675.

Sequence in context: A054885 A000449 A027274 * A016082 A003355 A247201

Adjacent sequences:  A253671 A253672 A253673 * A253675 A253676 A253677

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 08 2015

STATUS

approved

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Last modified November 26 09:38 EST 2020. Contains 338639 sequences. (Running on oeis4.)