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 A276599 Values of n such that n^2 + 5 is a triangular number (A000217). 5
 1, 4, 10, 25, 59, 146, 344, 851, 2005, 4960, 11686, 28909, 68111, 168494, 396980, 982055, 2313769, 5723836, 13485634, 33360961, 78600035, 194441930, 458114576, 1133290619, 2670087421, 6605301784, 15562409950, 38498520085, 90704372279, 224385818726 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1). FORMULA a(n) = 6*a(n-2)-a(n-4) for n>4. G.f.: x*(1+x)*(1+3*x+x^2) / ((1+2*x-x^2)*(1-2*x-x^2)). EXAMPLE 4 is in the sequence because 4^2+5 = 21, which is a triangular number. MATHEMATICA CoefficientList[Series[(1 + x)*(1 + 3*x + x^2)/((1 + 2*x - x^2)*(1 - 2*x - x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 07 2016 *) LinearRecurrence[{0, 6, 0, -1}, {1, 4, 10, 25}, 30] (* Harvey P. Dale, Feb 13 2017 *) PROG (PARI) Vec(x*(1+x)*(1+3*x+x^2)/((1+2*x-x^2)*(1-2*x-x^2)) + O(x^40)) (PARI) a(n)=([0, 1; -1, 6]^(n\2)*if(n%2, [1; 10], [-1; 4]))[1, 1] \\ Charles R Greathouse IV, Sep 07 2016 CROSSREFS Cf. A000217, A230044. Cf. A001109 (k=0), A106328 (k=1), A077241 (k=2), A276598 (k=3), A276600 (k=6), A276601 (k=9), A276602 (k=10), where k is the value added to n^2. Sequence in context: A159297 A248731 A279101 * A281867 A298806 A033539 Adjacent sequences:  A276596 A276597 A276598 * A276600 A276601 A276602 KEYWORD nonn,easy AUTHOR Colin Barker, Sep 07 2016 STATUS approved

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Last modified August 10 03:47 EDT 2020. Contains 336368 sequences. (Running on oeis4.)