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 A108099 a(n) = 8n^2 + 8n + 4. 7
 4, 20, 52, 100, 164, 244, 340, 452, 580, 724, 884, 1060, 1252, 1460, 1684, 1924, 2180, 2452, 2740, 3044, 3364, 3700, 4052, 4420, 4804, 5204, 5620, 6052, 6500, 6964, 7444, 7940, 8452, 8980, 9524, 10084, 10660, 11252, 11860, 12484, 13124, 13780, 14452, 15140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Also the number for Waterman [polyhedra] have a unit rhombic dodecahedron face so sqrt 4, sqrt 20, sqrt 52, etc...and a one-to-one match...that is, no omissions and no extras. - Steve Waterman and Roger Kaufman (swaterman(AT)watermanpolyhedron.com), Apr 02 2009. [This sentence makes no sense - some words must have been dropped. - N. J. A. Sloane, Jun 12 2014] Also, sequence found by reading the segment (4, 20) together with the line from 20, in the direction 20, 52, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 2011 Sum of consecutive even squares: (2*n)^2 + (2*n+2)^2 = 8*n^2 + 8*n + 4. - Michel Marcus, Jan 27 2014 LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Adrian Rossiter, Antiprism Steve Waterman, Polyhedra Project Steve Waterman, Waterman's Polyhedral Mensuration chart Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 8*n^2 + 8*n + 4. G.f.: 4*(1+2*x+x^2)/(1-x)^3. a(n) = 16*n+a(n-1), a(0)=4. - Vincenzo Librandi, Nov 13 2010 a(n) = A069129(n+1) + 3. - Omar E. Pol, Sep 04 2011 a(n) = A035008(n) + 4. - Omar E. Pol, Jun 12 2014 MAPLE A108099:=n->8*n^2 + 8*n + 4; seq(A108099(n), n=0..50); # Wesley Ivan Hurt, Jun 09 2014 MATHEMATICA CoefficientList[Series[-(4*(z^2 + 2*z + 1))/(z - 1)^3, {z, 0, 100}], z] (* and *) Table[8*n*(n + 1) + 4, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 17 2011 *) PROG (PARI) a(n)=8*n^2+8*n+4 \\ Charles R Greathouse IV, Jul 17 2011 (MAGMA) [ 8*n^2 + 8*n + 4 : n in [0..50] ]; // Wesley Ivan Hurt, Jun 09 2014 CROSSREFS Cf. A016742. Sequence in context: A294630 A160799 A187274 * A244050 A250224 A250272 Adjacent sequences:  A108096 A108097 A108098 * A108100 A108101 A108102 KEYWORD nonn,easy AUTHOR Dorthe Roel (dorthe_roel(AT)hotmail.com or dorthe.roel1(AT)skolekom.dk), Jun 07 2005 STATUS approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)