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 A253475 Indices of centered square numbers (A001844) which are also centered hexagonal numbers (A003215). 3
 1, 6, 55, 540, 5341, 52866, 523315, 5180280, 51279481, 507614526, 5024865775, 49741043220, 492385566421, 4874114620986, 48248760643435, 477613491813360, 4727886157490161, 46801248083088246, 463284594673392295, 4586044698650834700, 45397162391834954701 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also positive integers x in the solutions to 4*x^2 - 6*y^2 - 4*x + 6*y = 0, the corresponding values of y being A054318. Also indices of centered hexagonal numbers (A003215) which are also hexagonal numbers (A000384). Also indices of terms in sequence A193218 which are the square root of a sum of 5th powers (A000539). - Daniel Poveda Parrilla, Jun 10 2017 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (11,-11,1). FORMULA a(n) = 11*a(n-1)-11*a(n-2)+a(n-3). G.f.: x*(5*x-1) / ((x-1)*(x^2-10*x+1)). a(n) = sqrt((-2-(5-2*sqrt(6))^n-(5+2*sqrt(6))^n)*(2-(5-2*sqrt(6))^(1+n)-(5+2*sqrt(6))^(1+n)))/(4*sqrt(2)). - Gerry Martens, Jun 04 2015 EXAMPLE 6 is in the sequence because the 6th centered square number is 61, which is also the 5th centered hexagonal number. PROG (PARI) Vec(x*(5*x-1)/((x-1)*(x^2-10*x+1)) + O(x^100)) CROSSREFS Cf. A000384, A000539, A001844, A003215, A054318, A193218, A253175. Sequence in context: A295548 A198855 A318592 * A215853 A110431 A121661 Adjacent sequences:  A253472 A253473 A253474 * A253476 A253477 A253478 KEYWORD nonn,easy AUTHOR Colin Barker, Jan 02 2015 STATUS approved

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Last modified November 23 17:02 EST 2020. Contains 338590 sequences. (Running on oeis4.)