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!)
 A155883 a(n) = 14*n^3 - 30*n^2 + 24*n - 7. 2
 1, 33, 173, 505, 1113, 2081, 3493, 5433, 7985, 11233, 15261, 20153, 25993, 32865, 40853, 50041, 60513, 72353, 85645, 100473, 116921, 135073, 155013, 176825, 200593, 226401, 254333, 284473, 316905, 351713, 388981, 428793, 471233, 516385, 564333, 615161, 668953 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name was: The sequence gives the three-dimensional forms of the centered hexagonal numbers. Two examples: its third term 173 is built 19 + 37 + 61 + 37 + 19 and its fourth term 505 is built 37 + 61 + 91 + 127 + 91 + 61 + 37. The sequence's digital roots run through 1, 6, 2. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 David Z. Crookes, De Pulchritudine Numerorum Figuratorum (On the Beauty of Figurate Numbers), Mathematics in School (May, 1988), 38-39. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 14*n^3 - 30*n^2 + 24*n - 7. G.f.: x*(1+29*x+47*x^2+7*x^3)/(1-x)^4. [Colin Barker, Jun 16 2012] a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 30 2012 MATHEMATICA CoefficientList[Series[(1+29*x+47*x^2+7*x^3)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 30 2012 *) PROG (MAGMA) I:=[1, 33, 173, 505]; [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, Jun 30 2012 CROSSREFS Sequence in context: A172077 A180943 A113752 * A071914 A279867 A230650 Adjacent sequences:  A155880 A155881 A155882 * A155884 A155885 A155886 KEYWORD nonn,easy,less AUTHOR David Z. Crookes, Jan 29 2009 EXTENSIONS More terms from Colin Barker, Jun 16 2012 New name using explicit formula from Joerg Arndt, Jan 15 2021 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 11 00:03 EDT 2021. Contains 342877 sequences. (Running on oeis4.)