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 A253920 Indices of centered octagonal numbers (A016754) which are also heptagonal numbers (A000566). 3
 1, 5, 39, 760, 6494, 55518, 1095199, 9363623, 80056197, 1579275478, 13502337152, 115440979836, 2277314143357, 19470360808841, 166465812866595, 3283885415444596, 28076246784010850, 240043586712649434, 4735360491756963355, 40485928392182836139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also positive integers y in the solutions to 5*x^2 - 8*y^2 - 3*x + 8*y - 2 = 0, the corresponding values of x being A046195. LINKS Colin Barker, Table of n, a(n) for n = 1..950 Index entries for linear recurrences with constant coefficients, signature (1,0,1442,-1442,0,-1,1). FORMULA a(n) = a(n-1)+1442*a(n-3)-1442*a(n-4)-a(n-6)+a(n-7). G.f.: x*(4*x^5+34*x^4+721*x^3-34*x^2-4*x-1) / ((x-1)*(x^6-1442*x^3+1)). EXAMPLE 5 is in the sequence because the 5th centered octagonal number is 81, which is also the 6th heptagonal number. MATHEMATICA CoefficientList[Series[(4 x^5 + 34 x^4 + 721 x^3 - 34 x^2 -4 x - 1)/((x-1) (x^6 - 1442 x^3 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *) LinearRecurrence[{1, 0, 1442, -1442, 0, -1, 1}, {1, 5, 39, 760, 6494, 55518, 1095199}, 20] (* Harvey P. Dale, Jul 04 2017 *) PROG (PARI) Vec(x*(4*x^5+34*x^4+721*x^3-34*x^2-4*x-1)/((x-1)*(x^6-1442*x^3+1)) + O(x^100)) (Magma) I:=[1, 5, 39, 760, 6494, 55518, 1095199]; [n le 7 select I[n] else Self(n-1)+1442*Self(n-3)-1442*Self(n-4)-Self(n-6)+Self(n-7): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015 CROSSREFS Cf. A000566, A016754, A046195, A036354. Sequence in context: A193118 A227636 A118991 * A156378 A220061 A299815 Adjacent sequences: A253917 A253918 A253919 * A253921 A253922 A253923 KEYWORD nonn,easy AUTHOR Colin Barker, Jan 19 2015 EXTENSIONS Corrected by Vincenzo Librandi, Jan 20 2015 STATUS approved

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Last modified June 22 13:43 EDT 2024. Contains 373571 sequences. (Running on oeis4.)