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 A253304 Numbers n such that the sum of the heptagonal numbers H(n) and H(n+1) is equal to the octagonal number O(m) for some m. 2
 1, 22, 77, 1376, 4785, 85302, 296605, 5287360, 18384737, 327731030, 1139557101, 20314036512, 70634155537, 1259142532726, 4378178086205, 78046522992512, 271376407189185, 4837625283003030, 16820959067643277, 299854721023195360, 1042628085786694001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also positive integers x in the solutions to 5*x^2-3*y^2+2*x+2*y+1 = 0, the corresponding values of y being A253305. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,62,-62,-1,1). FORMULA a(n) = a(n-1)+62*a(n-2)-62*a(n-3)-a(n-4)+a(n-5). G.f.: x*(3*x^3+7*x^2-21*x-1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)). EXAMPLE 1 is in the sequence because H(1)+H(2) = 1+7 = 8 = O(2). PROG (PARI) Vec(x*(3*x^3+7*x^2-21*x-1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100)) CROSSREFS Cf. A000566, A000567, A253305. Sequence in context: A282723 A003908 A075252 * A094844 A323251 A010010 Adjacent sequences: A253301 A253302 A253303 * A253305 A253306 A253307 KEYWORD nonn,easy AUTHOR Colin Barker, Dec 30 2014 STATUS approved

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Last modified May 21 02:29 EDT 2024. Contains 372720 sequences. (Running on oeis4.)