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 A252585 Numbers n such that the sum of the pentagonal numbers P(n) and P(n+1) is equal to the heptagonal number H(m) for some m. 2
 3, 234, 1617, 112948, 779551, 54440862, 375742125, 26240382696, 181106924859, 12647810018770, 87293162040073, 6096218188664604, 42075122996390487, 2938364519126320518, 20280121991098174821, 1416285602000697825232, 9774976724586323873395 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also positive integers x in the solutions to 6*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of y being A252586. LINKS Colin Barker, Table of n, a(n) for n = 1..745 Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1). FORMULA a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5). G.f.: x*(11*x^3+63*x^2-231*x-3) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)). EXAMPLE 3 is in the sequence because P(3)+P(4) = 12+22 = 34 = H(4). MATHEMATICA LinearRecurrence[{1, 482, -482, -1, 1}, {3, 234, 1617, 112948, 779551}, 20] (* Jean-François Alcover, Nov 13 2017 *) PROG (PARI) Vec(x*(11*x^3+63*x^2-231*x-3)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100)) CROSSREFS Cf. A000326, A000566, A252586. Sequence in context: A065580 A072320 A162603 * A339751 A053970 A298277 Adjacent sequences:  A252582 A252583 A252584 * A252586 A252587 A252588 KEYWORD nonn,easy AUTHOR Colin Barker, Dec 18 2014 STATUS approved

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Last modified June 20 09:40 EDT 2021. Contains 345162 sequences. (Running on oeis4.)