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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
OFFSET
1,2
COMMENTS
Also nonnegative integers x in the solutions to 10*x^2-4*y^2+4*x+2*y+2 = 0, the corresponding values of y being A252077.
FORMULA
a(n) = 1443*a(n-1)-1443*a(n-2)+a(n-3).
G.f.: 18*x^2*(11*x-27) / ((x-1)*(x^2-1442*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*x-27)/((x-1)*(x^2-1442*x+1)) + O(x^100)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 13 2014
STATUS
approved