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A253458 Indices of centered heptagonal numbers (A069099) which are also centered hexagonal numbers (A003215). 3
1, 13, 325, 8425, 218713, 5678101, 147411901, 3827031313, 99355402225, 2579413426525, 66965393687413, 1738520822446201, 45134575989913801, 1171760454915312613, 30420637251808214125, 789764808092098254625, 20503464373142746406113, 532300308893619308304301 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 6*x^2 - 7*y^2 - 6*x + 7*y = 0, the corresponding values of x being A253457.
LINKS
Giovanni Lucca, Circle Chains Inscribed in Symmetrical Lenses and Integer Sequences, Forum Geometricorum, Volume 16 (2016) 419-427.
FORMULA
a(n) = 27*a(n-1)-27*a(n-2)+a(n-3).
G.f.: -x*(x^2-14*x+1) / ((x-1)*(x^2-26*x+1)).
a(n) = 1/2+(13+2*sqrt(42))^(-n)*(7+sqrt(42)-(-7+sqrt(42))*(13+2*sqrt(42))^(2*n))/28. - Colin Barker, Mar 03 2016
EXAMPLE
13 is in the sequence because the 13th centered heptagonal number is 547, which is also the 14th centered hexagonal number.
MATHEMATICA
LinearRecurrence[{27, -27, 1}, {1, 13, 325}, 20] (* Harvey P. Dale, Oct 13 2022 *)
PROG
(PARI) Vec(-x*(x^2-14*x+1)/((x-1)*(x^2-26*x+1)) + O(x^100))
CROSSREFS
Sequence in context: A166743 A212733 A183803 * A012492 A296395 A183440
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 01 2015
STATUS
approved

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Last modified February 27 04:33 EST 2024. Contains 370362 sequences. (Running on oeis4.)