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 A007586 11-gonal (or hendecagonal) pyramidal numbers: n*(n+1)*(3*n-2)/2. (Formerly M4835) 10
 0, 1, 12, 42, 100, 195, 336, 532, 792, 1125, 1540, 2046, 2652, 3367, 4200, 5160, 6256, 7497, 8892, 10450, 12180, 14091, 16192, 18492, 21000, 23725, 26676, 29862, 33292, 36975, 40920, 45136, 49632, 54417, 59500, 64890, 70596, 76627, 82992, 89700, 96760, 104181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Starting with 1 equals binomial transform of [1, 11, 19, 9, 0, 0, 0, ...]. - Gary W. Adamson, Nov 02 2007 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 194. E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: x*(1+8*x)/(1-x)^4. a(0)=0, a(1)=1, a(2)=12, a(3)=42; for n>3, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Harvey P. Dale, Apr 09 2012 a(n) = Sum_{i=0..n-1}  (n-i)*(9*i+1), with a(0)=0. - Bruno Berselli, Feb 10 2014 From Amiram Eldar, Jun 28 2020: (Start) Sum_{n>=1} 1/a(n) = (9*log(3) + sqrt(3)*Pi - 4)/10. Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(3)*Pi + 2 - 4*log(2))/5. (End) EXAMPLE From Vincenzo Librandi, Feb 12 2014: (Start) After 0, the sequence is provided by the row sums of the triangle (see above, third formula):   1;   2, 10;   3, 20, 19;   4, 30, 38, 28;   5, 40, 57, 56, 37;   6, 50, 76, 84, 74, 46; etc. (End) MAPLE seq(n*(n+1)*(3*n-2)/2, n=0..45); # G. C. Greubel, Aug 30 2019 MATHEMATICA Table[n(n+1)(3n-2)/2, {n, 0, 45}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 1, 12, 42}, 45] (* Harvey P. Dale, Apr 09 2012 *) CoefficientList[Series[x(1+8x)/(1-x)^4, {x, 0, 45}], x] (* Vincenzo Librandi, Feb 12 2014 *) PROG (MAGMA) I:=[0, 1, 12, 42]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4) : n in [1..50]]; // Vincenzo Librandi, Feb 12 2014 (PARI) a(n)=n*(n+1)*(3*n-2)/2 \\ Charles R Greathouse IV, Oct 07 2015 (Sage) [n*(n+1)*(3*n-2)/2 for n in (0..45)] # G. C. Greubel, Aug 30 2019 (GAP) List([0..45], n-> n*(n+1)*(3*n-2)/2); # G. C. Greubel, Aug 30 2019 CROSSREFS Cf. A051682. Cf. A093644 ((9, 1) Pascal, column m=3). Cf. similar sequences listed in A237616. Sequence in context: A090554 A009948 A193068 * A228391 A334277 A122973 Adjacent sequences:  A007583 A007584 A007585 * A007587 A007588 A007589 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Vincenzo Librandi, Feb 12 2014 STATUS approved

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Last modified October 27 06:09 EDT 2020. Contains 338035 sequences. (Running on oeis4.)