The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A147875 Second heptagonal numbers: a(n) = n*(5*n+3)/2. 31
 0, 4, 13, 27, 46, 70, 99, 133, 172, 216, 265, 319, 378, 442, 511, 585, 664, 748, 837, 931, 1030, 1134, 1243, 1357, 1476, 1600, 1729, 1863, 2002, 2146, 2295, 2449, 2608, 2772, 2941, 3115, 3294, 3478, 3667, 3861, 4060, 4264, 4473, 4687, 4906, 5130, 5359, 5593 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Zero followed by partial sums of A016897. Apparently = every 2nd term of A111710 and A085787. Bisection of A085787. Sequence found by reading the line from 0, in the direction 0, 13,... and the line from 4, in the direction 4, 27,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 18 2012 Numbers of the form m^2 + k*m*(m+1)/2: in this case is k=3. See also A254963. - Bruno Berselli, Feb 11 2015 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: x*(4+x)/(1-x)^3. a(n) = Sum_{k=0..n-1} A016897(k). a(n) - a(n-1) = 5*n -1. - Vincenzo Librandi, Nov 26 2010 G.f.: U(0) where U(k)= 1 + 2*(2*k+3)/(k + 2 - x*(k+2)^2*(k+3)/(x*(k+2)*(k+3) + (2*k+2)*(2*k+3)/U(k+1)));(continued fraction, 3-step). - Sergei N. Gladkovskii, Nov 14 2012 E.g.f.: U(0) where U(k)= 1 + 2*(2*k+3)/(k + 2 - 2*x*(k+2)^2*(k+3)/(2*x*(k+2)*(k+3) + (2*k+2)^2*(2*k+3)/U(k+1))); (continued fraction, 3rd kind, 3-step). - Sergei N. Gladkovskii, Nov 14 2012 a(n) = A130520(5n+3). - Philippe Deléham, Mar 26 2013 a(n) = A131242(10n+7)/2. - Philippe Deléham, Mar 27 2013 a(0)=0, a(1)=4, a(2)=13, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 15 2013 Sum_{n>=1} 1/a(n) = 10/9 + sqrt(1 - 2/sqrt(5))*Pi/3 - 5*log(5)/6 + sqrt(5)*log((1 + sqrt(5))/2)/3 = 0.4688420784500060750083432... . - Vaclav Kotesovec, Apr 27 2016 a(n) = A000217(n) + A000217(2*n). - Bruno Berselli, Jul 01 2016 From Ilya Gutkovskiy, Jul 01 2016: (Start) E.g.f.: x*(8 + 5*x)*exp(x)/2. Dirichlet g.f.: (5*zeta(s-2) + 3*zeta(s-1))/2. (End) a(n) = A000566(-n) for all n in Z. - Michael Somos, Jan 25 2019 EXAMPLE G.f. = 4*x + 13*x^2 + 27*x^3 + 46*x^4 + 70*x^5 + 99*x^6 + 133*x^7 + ... - Michael Somos, Jan 25 2019 MATHEMATICA Table[(n(5n+3))/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 4, 13}, 50] (* Harvey P. Dale, May 15 2013 *) PROG (PARI) a(n)=n*(5*n+3)/2 \\ Charles R Greathouse IV, Sep 24 2015 (MAGMA) [n*(5*n+3)/2: n in [0..50]]; // G. C. Greubel, Jul 04 2019 (Sage) [n*(5*n+3)/2 for n in (0..50)] # G. C. Greubel, Jul 04 2019 (GAP) List([0..50], n-> n*(5*n+3)/2) # G. C. Greubel, Jul 04 2019 CROSSREFS Cf. A016897, A111710, A000217, A085787, A224419 (positions of squares). Second n-gonal numbers: A005449, A014105, A045944, A179986, A033954, A062728, A135705. Cf. A000566. Sequence in context: A304946 A316616 A119652 * A321988 A108753 A024970 Adjacent sequences:  A147872 A147873 A147874 * A147876 A147877 A147878 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Nov 16 2008 EXTENSIONS Edited by Klaus Brockhaus and R. J. Mathar, Nov 20 2008 New name from Bruno Berselli, Jan 13 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 22 07:15 EDT 2021. Contains 343162 sequences. (Running on oeis4.)