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A253446 Indices of centered heptagonal numbers (A069099) which are also centered octagonal numbers (A016754). 3
1, 16, 465, 13920, 417121, 12499696, 374573745, 11224712640, 336366805441, 10079779450576, 302057016711825, 9051630721904160, 271246864640412961, 8128354308490484656, 243579382390074126705, 7299253117393733316480, 218734014139421925367681 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 7*x^2 - 8*y^2 - 7*x + 8*y = 0, the corresponding values of y being A253447.

LINKS

Colin Barker, Table of n, a(n) for n = 1..678

Index entries for linear recurrences with constant coefficients, signature (31,-31,1).

FORMULA

a(n) = 31*a(n-1)-31*a(n-2)+a(n-3).

G.f.: x*(15*x-1) / ((x-1)*(x^2-30*x+1)).

a(n) = sqrt((-2-(15-4*sqrt(14))^n-(15+4*sqrt(14))^n)*(2-(15-4*sqrt(14))^(1+n)-(15+4*sqrt(14))^(1+n)))/(4*sqrt(7)).  - Gerry Martens, Jun 04 2015

EXAMPLE

16 is in the sequence because the 16th centered heptagonal number is 841, which is also the 15th centered octagonal number.

PROG

(PARI) Vec(x*(15*x-1)/((x-1)*(x^2-30*x+1)) + O(x^100))

CROSSREFS

Cf. A016754, A069099, A253447, A253514.

Sequence in context: A229583 A241077 A318937 * A159646 A113674 A281834

Adjacent sequences:  A253443 A253444 A253445 * A253447 A253448 A253449

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 01 2015

STATUS

approved

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Last modified July 24 14:51 EDT 2021. Contains 346273 sequences. (Running on oeis4.)