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 A005904 Centered dodecahedral numbers. (Formerly M5239) 7
 1, 33, 155, 427, 909, 1661, 2743, 4215, 6137, 8569, 11571, 15203, 19525, 24597, 30479, 37231, 44913, 53585, 63307, 74139, 86141, 99373, 113895, 129767, 147049, 165801, 186083, 207955, 231477, 256709, 283711, 312543, 343265, 375937, 410619, 447371, 486253, 527325 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Amiram Eldar, Table of n, a(n) for n = 0..10000 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992. Boon K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558; alternative link. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = (2*n+1)*(5*n^2+5*n+1). Sum_{n>=0} 1/a(n) = -psi((5+sqrt(5))/10) - psi((5-sqrt(5))/10) - 2*gamma - 4*log(2), where psi is the digamma function and gamma is Euler's constant (A001620). - Amiram Eldar, Sep 12 2022 MAPLE A005904:=(z+1)*(z**2+28*z+1)/(z-1)**4; [Conjectured by Simon Plouffe in his 1992 dissertation.] MATHEMATICA a[n_] := (2*n + 1) * (5*n^2 + 5*n + 1); Array[a, 30, 0] (* Amiram Eldar, Sep 12 2022 *) CROSSREFS Cf. A001620, A006566. Sequence in context: A084028 A283552 A007260 * A207078 A182588 A199900 Adjacent sequences: A005901 A005902 A005903 * A005905 A005906 A005907 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 9 02:22 EST 2022. Contains 358698 sequences. (Running on oeis4.)