

A252076


Numbers n such that the sum of the heptagonal numbers H(n) and H(n+1) is equal to the hexagonal number X(m) for some m.


2



0, 486, 701100, 1010986002, 1457841114072, 2102205875506110, 3031379414638696836, 4371247013703125331690, 6303335162380492089600432, 9089404932905655890078491542, 13106915609914793413001095203420, 18900163220092199195891689204840386
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OFFSET

1,2


COMMENTS

Also nonnegative integers x in the solutions to 10*x^24*y^2+4*x+2*y+2 = 0, the corresponding values of y being A252077.


LINKS

Colin Barker, Table of n, a(n) for n = 1..317
Index entries for linear recurrences with constant coefficients, signature (1443,1443,1).


FORMULA

a(n) = 1443*a(n1)1443*a(n2)+a(n3).
G.f.: 18*x^2*(11*x27) / ((x1)*(x^21442*x+1)).


EXAMPLE

486 is in the sequence because H(486)+H(487) = 589761+592192 = 1181953 = X(769).


MATHEMATICA

LinearRecurrence[{1443, 1443, 1}, {0, 486, 701100}, 20] (* Harvey P. Dale, Oct 13 2015 *)


PROG

(PARI) concat(0, Vec(18*x^2*(11*x27)/((x1)*(x^21442*x+1)) + O(x^100)))


CROSSREFS

Cf. A000384, A000566, A252077.
Sequence in context: A223412 A097765 A179428 * A178813 A178814 A178812
Adjacent sequences: A252073 A252074 A252075 * A252077 A252078 A252079


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Dec 13 2014


STATUS

approved



