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A253879 Indices of centered heptagonal numbers (A069099) which are also triangular numbers (A000217). 3
1, 9, 136, 2160, 34417, 548505, 8741656, 139317984, 2220346081, 35386219305, 563959162792, 8987960385360, 143243407002961, 2282906551662009, 36383261419589176, 579849276161764800, 9241205157168647617, 147279433238536597065, 2347229726659416905416 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers y in the solutions to x^2 - 7*y^2 + x + 7*y - 2 = 0, the corresponding values of x being A253878.

LINKS

Colin Barker, Table of n, a(n) for n = 1..832

Index entries for linear recurrences with constant coefficients, signature (17,-17,1).

FORMULA

a(n) = 17*a(n-1)-17*a(n-2)+a(n-3).

G.f.: x*(8*x-1) / ((x-1)*(x^2-16*x+1)).

a(n) = (14-(8-3*sqrt(7))^n*(7+3*sqrt(7))+(-7+3*sqrt(7))*(8+3*sqrt(7))^n)/28. - Colin Barker, Mar 04 2016

EXAMPLE

9 is in the sequence because the 9th centered heptagonal number is 253, which is also the 22nd triangular number.

PROG

(PARI) Vec(x*(8*x-1)/((x-1)*(x^2-16*x+1)) + O(x^100))

CROSSREFS

Cf. A000217, A069099, A253878, A253880.

Sequence in context: A188685 A052137 A003376 * A231757 A156975 A081876

Adjacent sequences:  A253876 A253877 A253878 * A253880 A253881 A253882

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 17 2015

STATUS

approved

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Last modified June 17 05:35 EDT 2019. Contains 324183 sequences. (Running on oeis4.)