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 A129556 Numbers n such that centered pentagonal number A005891(n) = (5n^2+5n+2)/2 is a perfect square. 11
 0, 2, 21, 95, 816, 3626, 31005, 137711, 1177392, 5229410, 44709909, 198579887, 1697799168, 7540806314, 64471658493, 286352060063, 2448225223584, 10873837476098, 92968086837717, 412919472031679, 3530339074609680, 15680066099727722, 134059916748330141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Corresponding numbers k>0 such that k^2 is a centered pentagonal number are listed in A129557(n) = {1, 4, 34, 151, 1291, 5734, 49024, ...}. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Centered Pentagonal Number Index entries for linear recurrences with constant coefficients, signature (1,38,-38,-1,1). FORMULA For n>=5, a(n) = 38*a(n-2) - a(n-4) + 18. - Max Alekseyev, May 08 2009 G.f.: x^2*(x^3+2*x^2-19*x-2) / ((x-1)*(x^2-6*x-1)*(x^2+6*x-1)). - Colin Barker, Feb 21 2013 a(n) = (A221874(n) - 1) / 2. - Bruno Berselli, Feb 21 2013 MAPLE A005891 := proc(n) (5*n^2+5*n+2)/2 ; end: n := 0 : while true do if issqr(A005891(n)) then print(n) ; fi ; n := n+1 ; od : # R. J. Mathar, Jun 06 2007 MATHEMATICA Do[ f=(5n^2+5n+2)/2; If[ IntegerQ[ Sqrt[f] ], Print[n] ], {n, 1, 40000} ] LinearRecurrence[{1, 38, -38, -1, 1}, {0, 2, 21, 95, 816}, 30] (* Harvey P. Dale, Nov 09 2017 *) PROG (PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -1, -38, 38, 1]^(n-1)*[0; 2; 21; 95; 816])[1, 1] \\ Charles R Greathouse IV, Feb 11 2019 CROSSREFS Cf. A005891 (centered pentagonal numbers), A129557 (numbers k>0 such that k^2 is a centered pentagonal number), A221874. Cf. numbers m such that k*A000217(m)+1 is a square: A006451 for k=1; m=0 for k=2; A233450 for k=3; A001652 for k=4; this sequence for k=5; A001921 for k=6. - Bruno Berselli, Dec 16 2013 Sequence in context: A034520 A111128 A213827 * A077209 A068045 A188530 Adjacent sequences:  A129553 A129554 A129555 * A129557 A129558 A129559 KEYWORD nonn,easy AUTHOR Alexander Adamchuk, Apr 20 2007 EXTENSIONS More terms from R. J. Mathar, Jun 06 2007 Formula and further terms from Max Alekseyev, May 08 2009 a(22)-a(23) from Colin Barker, Feb 21 2013 STATUS approved

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Last modified April 19 20:13 EDT 2021. Contains 343117 sequences. (Running on oeis4.)