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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247541 a(n) = 7*n^2 + 1. 1
 1, 8, 29, 64, 113, 176, 253, 344, 449, 568, 701, 848, 1009, 1184, 1373, 1576, 1793, 2024, 2269, 2528, 2801, 3088, 3389, 3704, 4033, 4376, 4733, 5104, 5489, 5888, 6301, 6728, 7169, 7624, 8093, 8576, 9073, 9584, 10109, 10648, 11201, 11768, 12349, 12944, 13553 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Michael De Vlieger, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (1 + 5*x + 8*x^2)/(1 - x)^3. - Vincenzo Librandi, Sep 19 2014 From Amiram Eldar, Jul 15 2020: (Start) Sum_{n>=0} 1/a(n) = (1 + (Pi/sqrt(7))*coth(Pi/sqrt(7)))/2. Sum_{n>=0} (-1)^n/a(n) = (1 + (Pi/sqrt(7))*csch(Pi/sqrt(7)))/2. (End) From Amiram Eldar, Feb 05 2021: (Start) Product_{n>=0} (1 + 1/a(n)) = sqrt(2)*csch(Pi/sqrt(7))*sinh(sqrt(2/7)*Pi). Product_{n>=1} (1 - 1/a(n)) = (Pi/sqrt(7))*csch(Pi/sqrt(7)). (End) E.g.f.: exp(x)*(1 + 7*x + 7*x^2). - Stefano Spezia, Feb 05 2021 MATHEMATICA a247541[n_Integer] := 7 n^2 + 1; a247541 /@ Range[0, 120] (* Michael De Vlieger, Sep 18 2014 *) CoefficientList[Series[(1 + 5 x + 8 x^2)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 19 2014 *) LinearRecurrence[{3, -3, 1}, {1, 8, 29}, 50] (* Harvey P. Dale, Jun 09 2015 *) PROG (Python) for n in range (0, 500) : print (7*n**2+1) (PARI) vector(100, n, 7*(n-1)^2+1) \\ Derek Orr, Sep 18 2014 (MAGMA) [7*n^2+1: n in [0..50]]; // Vincenzo Librandi, Sep 19 2014 CROSSREFS Cf. A201602 (primes of the form 7n^2 + 1). Sequence in context: A300310 A171442 A341402 * A320695 A093809 A244244 Adjacent sequences:  A247538 A247539 A247540 * A247542 A247543 A247544 KEYWORD nonn,easy AUTHOR Karl V. Keller, Jr., Sep 18 2014 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 December 6 10:24 EST 2021. Contains 349563 sequences. (Running on oeis4.)