This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A010003 a(0) = 1, a(n) = 11*n^2 + 2 for n>0. 1
 1, 13, 46, 101, 178, 277, 398, 541, 706, 893, 1102, 1333, 1586, 1861, 2158, 2477, 2818, 3181, 3566, 3973, 4402, 4853, 5326, 5821, 6338, 6877, 7438, 8021, 8626, 9253, 9902, 10573, 11266, 11981, 12718, 13477, 14258, 15061, 15886, 16733, 17602, 18493, 19406 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Apart from the first term, numbers of the form (r^2+2*s^2)*n^2+2 = (r*n)^2+(s*n-1)^2+(s*n+1)^2: in this case is r=3, s=1. After 13, all terms are in A000408. - Bruno Berselli, Feb 06 2012 LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (1+x)*(1+9*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012 E.g.f.: (x*(x+1)*11+2)*e^x-1. - Gopinath A. R., Feb 14 2012 MATHEMATICA Join[{1}, 11 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *) Join[{1}, LinearRecurrence[{3, -3, 1}, {13, 46, 101}, 50]] (* Vincenzo Librandi, Aug 03 2015 *) PROG (PARI) A010003(n)=11*n^2+2-!n   \\ M. F. Hasler, Feb 14 2012 (MAGMA) [1] cat [11*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015 CROSSREFS Cf. A206399. Sequence in context: A141549 A121964 A147208 * A007587 A219905 A034462 Adjacent sequences:  A010000 A010001 A010002 * A010004 A010005 A010006 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Bruno Berselli, Feb 06 2012 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 20:00 EST 2016. Contains 278986 sequences.