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 A015219 Odd tetrahedral numbers: a(n) = (4*n+1)*(4*n+2)*(4*n+3)/6. 11
 1, 35, 165, 455, 969, 1771, 2925, 4495, 6545, 9139, 12341, 16215, 20825, 26235, 32509, 39711, 47905, 57155, 67525, 79079, 91881, 105995, 121485, 138415, 156849, 176851, 198485, 221815, 246905, 273819, 302621, 333375, 366145, 400995, 437989 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Delbert L. Johnson, Table of n, a(n) for n = 0..19999 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA From Jaume Oliver Lafont, Oct 20 2009: (Start) G.f.: (1+x)*(1+30*x+x^2)/(1-x)^4. Sum_{n>=0} 1/a(n) = (3/2)*log(2). (End) From Ant King, Oct 19 2012: (Start) a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). a(n) = 64 + 3*a(n-1) - 3*a(n-2) + a(n-3). (End) a(n) = A000292(4*n+1). - L. Edson Jeffery, Jan 16 2013 a(n) = A000447(2*n+1). - Michel Marcus, Jan 25 2016 Sum_{n>=0} (-1)^n/a(n) = 3*(sqrt(2)-1)*Pi/4. - Amiram Eldar, Jan 04 2022 a(n) = A001505(n)/6. - R. J. Mathar, Apr 17 2024 MATHEMATICA LinearRecurrence[{4, -6, 4, -1}, {1, 35, 165, 455}, 35] (* Ant King, Oct 19 2012 *) Table[(4 n + 1) (4 n + 2) (4 n + 3)/6, {n, 0, 40}] (* Vincenzo Librandi, Jan 25 2016 *) PROG (PARI) a(n)=binomial(4*n+3, 3) \\ Charles R Greathouse IV, Jan 16 2013 (Magma) [(4*n+1)*(4*n+2)*(4*n+3)/6: n in [0..40]]; // Vincenzo Librandi, Jan 25 2016 CROSSREFS Cf. A000292, A000447. Sequence in context: A045614 A154074 A260867 * A195545 A270860 A228453 Adjacent sequences: A015216 A015217 A015218 * A015220 A015221 A015222 KEYWORD nonn,easy AUTHOR Mohammad K. Azarian EXTENSIONS More terms from Erich Friedman. STATUS approved

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Last modified August 14 16:37 EDT 2024. Contains 375166 sequences. (Running on oeis4.)