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 A069017 Triangular numbers of the form k^2 + k + 1. 6
 1, 3, 21, 91, 703, 3081, 23871, 104653, 810901, 3555111, 27546753, 120769111, 935778691, 4102594653, 31788928731, 139367449081, 1079887798153, 4734390674091, 36684396208461, 160829915470003, 1246189583289511, 5463482735306001, 42333761435634903 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1001 FORMULA G.f.: (x^4 +2*x^3 -16*x^2 +2*x +1)/((1-x)*(1-6*x+x^2)*(1+6*x+x^2)). From Zak Seidov, Sep 25 2010: (Start) a(n) = 34*a(n-2) - a(n-4) - 11. a(n) = 2*A124174(n) + 1. (End) a(n) = (A077443(n)^2 - 1)/2. - Amiram Eldar, Dec 01 2018 MAPLE Do[a = n(n + 1) + 1; b = Floor[Sqrt[2a]]; If[b(b + 1) == 2a, Print[a]], {n, 1, 106}] MATHEMATICA Select[Table[n^2+n+1, {n, 0, 206*10^6}], OddQ[Sqrt[8#+1]]&] (* The program takes a long time to run. *) (* Harvey P. Dale, Sep 22 2017 *) CoefficientList[Series[(x^4 +2*x^3 -16*x^2 +2*x +1)/((1-x)*(1-6*x+x^2)*(1+6*x+x^2)), {x, 0, 50}], x] (* G. C. Greubel, Dec 01 2018 *) PROG (PARI) Vec((x^4+2*x^3-16*x^2+2*x+1)/((1-x)*(1-6*x+x^2)*(1+6*x+x^2)) +O(x^66)) /* Joerg Arndt, Mar 25 2013 */ (MAGMA) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (x^4 +2*x^3 -16*x^2 +2*x +1)/((1-x)*(1-6*x+x^2)*(1+6*x+x^2)) )); // G. C. Greubel, Dec 01 2018 (Sage) s=((x^4 +2*x^3 -16*x^2 +2*x +1)/((1-x)*(1-6*x+x^2)*(1+6*x+x^2))).series(x, 50); s.coefficients(x, sparse=False) # G. C. Greubel, Dec 01 2018 CROSSREFS Cf. A124174. Sequence in context: A129755 A059826 A108970 * A264246 A144883 A074597 Adjacent sequences:  A069014 A069015 A069016 * A069018 A069019 A069020 KEYWORD nonn AUTHOR Amarnath Murthy, Apr 02 2002 EXTENSIONS Program and terms from Robert G. Wilson v a(18)-a(22) from Alex Ratushnyak, Mar 23 2013 STATUS approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)