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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 (list; graph; refs; listen; history; text; internal format)
 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. 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(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 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

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Last modified November 28 01:24 EST 2021. Contains 349396 sequences. (Running on oeis4.)