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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
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.
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 17 2015
STATUS
approved