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 A193252 Great rhombicuboctahedron with faces of centered polygons. 2
 1, 75, 365, 1015, 2169, 3971, 6565, 10095, 14705, 20539, 27741, 36455, 46825, 58995, 73109, 89311, 107745, 128555, 151885, 177879, 206681, 238435, 273285, 311375, 352849, 397851, 446525, 499015, 555465, 616019, 680821, 750015, 823745, 902155, 985389, 1073591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence starts with a central dot and expands outward with (n-1) centered polygonal pyramids producing a great rhombicosidodecahedron. Each iteration requires the addition of (n-2) edge units and (n-1) vertices to complete the centered polygon of each face: centered squares, centered octagons and centered hexagons. LINKS Bruno Berselli, Table of n, a(n) for n = 1..1000 OEIS Wiki, (Centered polygons) pyramidal numbers Wikipedia, Tetrahedral number Wikipedia, Triangular number Wikipedia, Centered polygonal number Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 24*n^3 - 36*n^2 + 14*n - 1. G.f.: x*(1+x)*(1+70*x+x^2)/(1-x)^4; a(n) = (2*n-1)*A069190(n). - Bruno Berselli, Jul 21 2011 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=75, a(2)=365, a(3)=1015. - Harvey P. Dale, Jul 27 2011 a(n) = 72 * A000330(n-1) + A005408(n-1). - Bruce J. Nicholson, Feb 23 2019 E.g.f.: 1 + (-1 + 2*x + 36*x^2 + 24*x^3)*exp(x). - G. C. Greubel, Feb 26 2019 MATHEMATICA Table[24n^3-36n^2+14n-1, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 75, 365, 1015}, 40] (* Harvey P. Dale, Jul 27 2011 *) PROG (Excel) =24*ROW()^3-36*ROW()^2+14*ROW()-1 (MAGMA) A069190:=func; [(2*n-1)*A069190(n): n in [1..40]];  // Bruno Berselli, Jul 21 2011 (PARI) for(n=1, 40, print1(24*n^3-36*n^2+14*n-1", "));  \\ Bruno Berselli, Jul 21 2011 (Sage) [24*n^3 -36*n^2 +14*n -1 for n in (1..40)] # G. C. Greubel, Feb 26 2019 (GAP) List([1..40], n-> 24*n^3 -36*n^2 +14*n -1) # G. C. Greubel, Feb 26 2019 CROSSREFS First differences in 2*A158591. Cf. A001844 (centered square numbers), A016754 (centered octagonal numbers), A003215 (centered hexagonal numbers). Sequence in context: A226741 A223078 A055561 * A223452 A015223 A129625 Adjacent sequences:  A193249 A193250 A193251 * A193253 A193254 A193255 KEYWORD nonn,easy,changed AUTHOR Craig Ferguson, Jul 19 2011 STATUS approved

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Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)