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A253714 Indices of hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099). 3
1, 2857, 45529, 184300369, 2937241777, 11889953986681, 189493215939721, 767068491312421537, 12224965330197902689, 49486656636639609035209, 788681413122894278122297, 3192582165489099245985035761, 50880992673985436128583949841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also positive integers x in the solutions to 4*x^2-7*y^2-2*x+7*y-2 = 0, the corresponding values of y being A253715.

LINKS

Colin Barker, Table of n, a(n) for n = 1..416

Index entries for linear recurrences with constant coefficients, signature (1,64514,-64514,-1,1).

FORMULA

a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+2856*x^3-21842*x^2+2856*x+1) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)).

EXAMPLE

2857 is in the sequence because the 2857th hexagonal number is 16322041, which is also the 2160th centered heptagonal number.

PROG

(PARI) Vec(-x*(x^4+2856*x^3-21842*x^2+2856*x+1)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^100))

CROSSREFS

Cf. A000384, A069099, A253715, A253716.

Sequence in context: A233788 A250637 A067703 * A031603 A236586 A233379

Adjacent sequences:  A253711 A253712 A253713 * A253715 A253716 A253717

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 10 2015

STATUS

approved

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Last modified April 18 07:59 EDT 2021. Contains 343084 sequences. (Running on oeis4.)